no, albums don't show up in the recently deleted album. I'm pretty sure when an album is deleted its gone for good
Yes that is probably right. Sorry I didn't pick up in your OP that it was albums rather than photos you had lost.
All the photos in the lost albums will still be there. Deleting albums does not delete any photos.But if you manually deleted some photos as well, they may be.
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So I use iCloud photo library. I wanted to remove the library from my iPhone. I turned it off in the settings on my iPhone. This deleted 95 percent of the photos off my phone and then there was a couple hundred left along with some albums. I waited for a while but those hung around. I deleted them off my phone manually and i made sure iCloud Photo Library was turned off.
This proceeded to delete these albums from the iCloud Photo Library on my computer
Is there any way to retrieve these besides a time machine backup?
and if I do decide to go with a time machine backup restore, how do clear out iCloud so it doesn't just immediately overwrite the restore?
Turning off iCloud Photo Library on your phone should not have had any effect on the library on your computer, but the last step where you manually deleted the stuff which hung around may have done. I don't know how long you waited, but iCloud Photos Library activity takes a long time. It may have been still turning itself off or preparing to turn off when you manually deleted. Too late now.
I have never restored an iCPL from Time Machine, but I believe that if you have two libraries on your computer and initially one is the iCloud Library, then you change it to be the other, it will merge the two on iCloud. iCloud Photos Library is supposed to avoid duplicates (but probably plenty of example where it hasn't...duplicates happen for different reasons).
So I think if you restore the Photos library from Time Machine, and then make the restored one your iCPL, it would merge with what is there and not duplicate. Your albums should be back.
There are a lot of ifs and buts in all this, and risks. Assuming the lost albums would take a lot of work to recreate, in your shoes I would back everything up in duplicate and try what I have outlined.