Since you’re new to this and therefore probably haven’t set up too much infrastructure yet, let me put in a plug for ZFS for the file system underlying your data. That will unlock for you snapshots and the ability to send very efficient backups off site to another ZFS pool.
There are commercial offerings for all this (I think rsync.net will give you a ZFS target), but I essentially have a second NAS set up at another location for the purpose.
Beyond that, I’m also a big fan of BackBlaze B2, which can give you object-based online storage.
As far as what to back up, that’ll depend on your setup. I usually find it simplest to backup my entire VM and do recovery by restoring the VM.
I’d just give it time. Let the account sit unused and set any messages to be forwarded to your new account. If you don’t notice anything in the next year or so, you probably won’t miss anything that might still be linked.