I'm probably just confused but it seems like there is two different things going on here. However this message is just a generic prompt that you'll always see when you turn off Messages in iCloud.
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I'm NOT saying people aren't experiencing problems. I am saying nothing can be determined from the above message.
Messages in iCloud is exactly that. Messages in iCloud. It saves storage space on the device by being able to utilize a copy of the data in the iCloud. And since its external of iCloud Backups it saves iCloud space if you have multiple devices by saving 1 database for messages and its attachments vs multiples from each device in an iCloud backup.
Once a message attachment is uploaded to iCloud and some other criteria is met the iPhone will cache ('Other' data) the attachment. The attachments are still on the iPhone so even if you don't have wireless data they will pop back up in full resolution if you go looking for them. If you look at old messages you will see a brief delay before they pop up even if the device is in AirPlane mode because its pulling the data from cache back into the app.
This is why the physical storage used by Messages varies between devices and varies between iCloud even though they appear identical to each other...
My iCloud storage (I delete my messages occasionally)
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My iPhone 11 Pro Max storage..
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However in the event your iPhone needs storage space the cached attachment can be deleted and that space utilized for new data. If this happens and you look at that attachment again it will redownload from iCloud. If conditions are just right (or just wrong) you'll even see a "Tap to Download" icon where the attachment is.
Anyway back to the generic 'Disable and Download" message. When a shared database is established especially one where client devices can be the sole resource for particular data (iPhone and SMS for example) there is a bit of setup required. Conversely removing (disabling) a device from a shared group can't just stop sharing, it needs to let the rest of the devices and iCloud know what to do and how to handle messages without it thus "Disable and Download".
Don't take my word for it though...These are some screen shots from a brand new iPhone SE on a brand new AppleID using a brand new email (I'm setting it up for a new hire at work). Messages in iCloud is turned off and has never been turned on on this AppleID/iCloud account. There isn't a single Message in the Messages app. And because of those two things there isn't even a Messages section in iCloud. Aka there is nothing to sync and nothing to upload/download.
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If I turn Messages in iCloud on and right back off as fast as I can toggle the switch....
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Still get the message when there isn't any user data to sync.
Point of all that rambling, its a wild goose chase to worry about that particular message. It will pop up regardless of whether there is an issue or not.
Generic iCloud syncing issue solutions.....
Unfortunately, upgrading an iPhone (replacing the host for a lot of the Message data) doesn't always go smooth. Especially if the database wasn't updated properly due to user error, network error, bug in software, etc etc..
Its normal to notice SMS text messages not playing as nice as iMessages. Its also normal to have different SMS on different devices especially if its spam you deleted from your iPhone the moment you got it.
First thing I would suggest is going to iCloud.com and making sure all the devices on the account are still owned and accessible by you. Remove devices you don't use anymore especially those with Message functionality. And of course the opposite applies, make sure your devices that should be there, are there.
Make sure you are closing and reopening (close from multitask window) the message app while diagnosing. This will trigger a sync because its easy to work faster then data can sync between all devices (in MacOS there is a Sync button in Message Preferences).
You can try to pinpoint which device isn't playing nice by deleting a text on one device and see if the others delete it, keep rotating devices to see if one stands out. If one does stand out, you might be able to compare them and see if there isn't something that doesn't line up. Delete anomalies, like messages on you iPad that aren't showing on your Mac and iPhone (for example I don't know if you own those). This happened with my iPad once, it just wouldn't sync "deletes" from other devices. Maybe see if one device is getting messages but at a clear and measurable different time then the rest.
I hate to suggest this because it is a pain in the ass especially if you use Apple Wallet with various credit cards....but log out of your AppleID/iCloud on devices having the issue and power cycle each device and then log back in. This CAN correct device syncing issues by running everything through all Apples checks, verifications and authorizations. Just do one device at a time so you aren't logged out on everything. Since its a database syncing across devices the one you notice the problem on isn't necessarily the one not syncing properly. This fixed my iPad where messages would not delete from it if I was deleting them from another device.
Good luck!
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I'm NOT saying people aren't experiencing problems. I am saying nothing can be determined from the above message.
Messages in iCloud is exactly that. Messages in iCloud. It saves storage space on the device by being able to utilize a copy of the data in the iCloud. And since its external of iCloud Backups it saves iCloud space if you have multiple devices by saving 1 database for messages and its attachments vs multiples from each device in an iCloud backup.
Once a message attachment is uploaded to iCloud and some other criteria is met the iPhone will cache ('Other' data) the attachment. The attachments are still on the iPhone so even if you don't have wireless data they will pop back up in full resolution if you go looking for them. If you look at old messages you will see a brief delay before they pop up even if the device is in AirPlane mode because its pulling the data from cache back into the app.
This is why the physical storage used by Messages varies between devices and varies between iCloud even though they appear identical to each other...
My iCloud storage (I delete my messages occasionally)
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My iPhone 11 Pro Max storage..
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However in the event your iPhone needs storage space the cached attachment can be deleted and that space utilized for new data. If this happens and you look at that attachment again it will redownload from iCloud. If conditions are just right (or just wrong) you'll even see a "Tap to Download" icon where the attachment is.
Anyway back to the generic 'Disable and Download" message. When a shared database is established especially one where client devices can be the sole resource for particular data (iPhone and SMS for example) there is a bit of setup required. Conversely removing (disabling) a device from a shared group can't just stop sharing, it needs to let the rest of the devices and iCloud know what to do and how to handle messages without it thus "Disable and Download".
Don't take my word for it though...These are some screen shots from a brand new iPhone SE on a brand new AppleID using a brand new email (I'm setting it up for a new hire at work). Messages in iCloud is turned off and has never been turned on on this AppleID/iCloud account. There isn't a single Message in the Messages app. And because of those two things there isn't even a Messages section in iCloud. Aka there is nothing to sync and nothing to upload/download.
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If I turn Messages in iCloud on and right back off as fast as I can toggle the switch....
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Still get the message when there isn't any user data to sync.
Point of all that rambling, its a wild goose chase to worry about that particular message. It will pop up regardless of whether there is an issue or not.
Generic iCloud syncing issue solutions.....
Unfortunately, upgrading an iPhone (replacing the host for a lot of the Message data) doesn't always go smooth. Especially if the database wasn't updated properly due to user error, network error, bug in software, etc etc..
Its normal to notice SMS text messages not playing as nice as iMessages. Its also normal to have different SMS on different devices especially if its spam you deleted from your iPhone the moment you got it.
First thing I would suggest is going to iCloud.com and making sure all the devices on the account are still owned and accessible by you. Remove devices you don't use anymore especially those with Message functionality. And of course the opposite applies, make sure your devices that should be there, are there.
Make sure you are closing and reopening (close from multitask window) the message app while diagnosing. This will trigger a sync because its easy to work faster then data can sync between all devices (in MacOS there is a Sync button in Message Preferences).
You can try to pinpoint which device isn't playing nice by deleting a text on one device and see if the others delete it, keep rotating devices to see if one stands out. If one does stand out, you might be able to compare them and see if there isn't something that doesn't line up. Delete anomalies, like messages on you iPad that aren't showing on your Mac and iPhone (for example I don't know if you own those). This happened with my iPad once, it just wouldn't sync "deletes" from other devices. Maybe see if one device is getting messages but at a clear and measurable different time then the rest.
I hate to suggest this because it is a pain in the ass especially if you use Apple Wallet with various credit cards....but log out of your AppleID/iCloud on devices having the issue and power cycle each device and then log back in. This CAN correct device syncing issues by running everything through all Apples checks, verifications and authorizations. Just do one device at a time so you aren't logged out on everything. Since its a database syncing across devices the one you notice the problem on isn't necessarily the one not syncing properly. This fixed my iPad where messages would not delete from it if I was deleting them from another device.
Good luck!