OP wrote " I read somewhere on this forum that factory reset didn't help them but that was only 1 case that I found. "
Most probably that user may have used Setup Asset and Migrated ALL their previous data, applications etc back into the Pristine and Virginal re-installation
Issues that may have existed when the TM Backup was made would have been migrated to the New Installation
A Factory Reset ?
There are two very distinct Factory Resets
Both will remove the " system data "
One is for Intel Computers and will involve Reinstalling the Operating System
For Apple Intel computers, use Disk Utility to erase an Intel-based Mac and then follow the instructions in How to reinstall macOS.
The Other for Apple Silicon M-Class computers will also remove the " System Data "
It Will Not Touch the existing and installed Operating System
For Apple Silicon computers, use Disk Utility to erase a Mac with Apple silicon