Does your laptop have an SD card slot? Maybe you could do a backup that way?
Once you get your backup sorted I would just do a fresh install of 22.1 Xia. You’ll be fine with that older hardware. I don’t think the new stuff from 20.3 to 22.1 would make you notice a severe difference. If you have 4 GB of RAM that’s your limiter, but I’d have said the same thing when 20.3 came out.
By not detected I assume you mean it didn’t auto-mount and show up in Nemo file browser. Maybe try running the Disks app in Linux Mint and see if your SD card shows up there and just needs to be reformatted?