Yes. Migration Assistant, if not flawless, works well. Use Time Machine, plug in a new SSD (as mentioned; you should have one for backup anyway) when asked if you want to format it, select OK, Go to Timemachine settings and select your SSD for TM to use. When setting up the new M4 you will be asked to migrate an old user account and you select the old account on the SSD, and it will migrate apps, documents, settings, passwords, licenses, bookmarks - everything, if you want. You can also select to migrate some of the stuff and leave out other.
I mostly use Migration Assistant, but once every few years, I choose to setup my whole mac from scratch. Often when there are big changes, like a big jump in macOS versions, big change in hardware, changes in users, what the mac will be used for etc. Seems like you are in much a situation like that, going from Intel to ARM and Catalina to Sequoia (!), likely a different size screen, lots of new versions of app you'll be needing to install anyway, and lots and lots of new mac features and functions that will require weeks to configure, anyway.
If I were you, I'd take it easy, one step at a time; start by just booting up the new mini and create a new user account. Get familiar with all the new things. I recommend
Macmost.com, their video library has an explanation on almost anything, presented in a clear, no-nonsense way. Take your time, just play around with stuff - you can at any time erase the mac, and it will start with the "hello" screen, like it came from the store. No need to reinstall or anything, it takes just a minute. So, experiment, test new things, no need to worry about screwing anything up.
If you feel that 'this is going well, I can start to install latest versions of my most important apps and copy over folders and documents' you do that - gradually, and you build up your new mac with it's own new setup.
(I haven't used TM for many years, I'm on CCC, so I'm not sure how easy it is to, say locate the 'music' folder on the TM SSD using the Finder, as I understand TM has a custom folder/file structure. But it's quick and easy to make a new volume on the SSD and just copy the user folder there, and use that for manual transfer.)
While waiting for your mini, you should try and read up on what's new in new macs and versions of macOS: (OSX is gone btw, it's now called macOS)
Keywords:
APFS, the new file system
SSV (Signed system volume).
(The startup disk is now two APFS 'volumes' in a 'volume group' where the SSV is locked and cannot be altered, and a "macHD - Data" volume, a normal volume that contains all user files and apps.)
SOC, "system-on-chip"
Thunderbolt 3, 4, 5 and USB 3.2 USB4 file transfer protocols
USB-C and Thunderbolt connnector types
I'm sure you are aware that both the internal drive and the RAM is soldered in, and not upgradable later. If not, you still have time to change your order.
I'm sure I forget something, but I bet someone will chime in if I do.
