And while MacOS sometimes has issues expediently clearing space the was previously used for snapshots, tools like DaisyDisk and others can force its hand if you need.
Bottom line, you don't lose available disk space by using Time Machine.
And yes, you can nuke snapshots preemptively, but often the first visible sign was Mail having corruption issues because it’s database was borked, at which point it was too late.
Migrating Time Machine backups from a USB drive to a network share is not supported, but it's doable, not impossible. (This is something I've done before, and in fact I'm doing this for family right now.)
If your Mac HD is that low on space, you're going to be getting horrible performance. You should sort that out and try to keep around 10% free.
Do NOT trust Time Machine. Back up your data.
And restore it once in a while.
"Backups not issue. Backups very boring. Restore is issue. Restore very exciting."
But yes, you need to check that it can restore every now and then.
Time Machine deletes old data. That is not a good backup plan.
Time Machine is not a long term backup, it’s a safety net.