You do not delete backup files, TimeMachine does not react well to Finder. I mean completely erase the drive in Disk Utilities which will destroy the data. That's why I advocated two backups: one to erase and re-establish as a TimeMachine drive; one to maintain what backups you do have. If you have only one backup, you now see the down side of that decision, no real backup when you may need it most.
Here's the point, by your own admission, backing up is not working. What do you have to lose? Old out-of-date data? It's your choice, but yes erasure destroys data. Depending on your drive, the erase and re-establish TM could take let's say and hour. How likely is it your Mac will have a fatal error that deletes all you internal drive's data in that hour? Not likely at all if the machine has been operating normally. But that's your choice, I'm just stating options.
As a hedge against disaster, maybe copy off your most critical files and fondest memories to iCloud or some smaller external drive you know to be good. Just something to at least partially protect yourself.
All this may be the fault of a malfunctioning OS. That can usually be fixed by reinstallation. Again, working backups, protect you in that event too.
You need to assess your situation and make your best decision. And as is the usual case, some other user here may have a whole different take. Let's hope they chime in with their thoughts.