Time machine will not show all available backups when trying to migrate, Please help with External SSD OS

Hello community.

I have finally successfully added Yosemite onto an external SSD so I can run my old Adobe CS5 suite. I am trying to migrate from time machine and I know I have other backups because when I try and run time machine from restore mode on start up it will show the older Mojave backups. All I get is one backup, the latest backup from monterey. Why does this migration tool not show the other backups on the time machine drive? When I choose this it loads everything from monterey so nothing works and I get a bunch of ???????? across the tool bar, it will not show the drive or anything in finder either. I manually moved the applications from the internal HD to the external HD and they moved successfully however Adobe now says I need to uninstall and reinstall.

A few other possible issues I was thinking of is the fact I have the old Yosemite OS on this external. Do I need Mojave on this external drive in order to see the backups to migrate? I feel like this isn't true since I can see the latest Monterey backup but I still wanted to ask. Plus I tried to upgrade to Mojave on the external OS but apple keeps telling me that my apple ID in incorrect even though on my phone it tells me I just signed into my apple ID. I can sign into the cloud on the computer but the app store keeps telling me I am wrong. I do not know how to get around this.

I have tried to restore the external SSD using time machine from cmommand + R on startup but this function has never worked. It just becomes stuck at the final process on reboot and will do nothing.

All I want to do is run an older OS on an external drive to run the Adobe CS5 creative software. I cannot find my original disc but I was hoping I could migrate the software but I keep hitting road blocks. if someone has the time to help walk me through actually making this work without having to reload the software that would be awesome. I am almost to the point of buying a used copy from someone to run.

Why I want to run CS5 and not the new subscription from adobe?

For one I think it's a total crap of a scheme to pay a subscription for software but that's the way our unfortunate world has gone to guarantee that income to these businesses. I was once a professional photographer for many years but I no longer do it for a living so I am fine with using my old CS5. So no I am NOT making money using photoshop or on my camera equipment.