You clearly have a bigger problem than I suspected.
My recommendation at this point would be to do a total backup, erase your drive, then reinstall the OS. After that, you can migrate your backup onto the fresh OS drive, while perhaps crossing your fingers and praying.
Let me add a few caveats at this point:
I had some bad experiences with Time Machine, which caused me to abandon it completely. It’s not reliable enough in critical situations like this. You can do a total backup, where everything looks fine, then the restore fails with some strange error. After this happened to me a couple of times, I totally gave up on it, and have been using Carbon Copy Cloner ever since. There are other similar backup options available. Since getting CCC, I’ve gone back to the old-fashioned backup methods I learned early in my career. A recent one, an older one, and an even older one. And since I now have multiple Macs, I can use one to restore the other if things go especially bad.
Before doing anything this drastic, you need to assess your own abilities. If things go bad, can you deal with it? Or would you want to take it to an expert? If you think you might end up taking it to an expert, do that now. For my own relatives and friends, I’m the expert. When they get a problem like this, I take over and do it all myself. I have the equipment (software & hardware) and knowledge to handle virtually anything that might happen.
Sorry I can’t be of more help. If you have a local Apple store, you could consider going to them. More than anything, you need to have several backups of your data. If you don’t already, do that ASAP.