Thank you for your help, I think I was able to resolve most of the errors :).
We had set a "Hardware Inventory Class" in the "Default Client settings" (Administration, Client Settings) which was not working anymore. I don't know if it was a custom one, but the name was something with pOffice. There was the following error in the SMS_Inventory_Data_Loader -->
Microsoft SQL Server reported SQL message 8152, severity 16: [Microsoft][SQL Server Native Client 11.0][SQL Server]String or binary data would be truncated. : pOFFICE_PRODUCTINFO_DATA
Please refer to your Configuration Manager documentation, SQL Server documentation, or the Microsoft Knowledge Base for further troubleshooting information.
After I removed this Class, the errors decreased more and more. At the moment we still get errors sometimes, but that's probably normal and everything works so far and is green (PXE, primary user, software assignment, hardware inventory etc.). We also had to define some exclusions in our Antivirus (folders and file types like mif, ddr etc.). But most of the exclusions were already made before, except for the MIF one.
What I also saw was the following:
If the AV was off, the Windows Defender Advanced Threat Protection was still running and also investigating files in the inboxes folder (used procmon for that). These files were the same ones, that SCCM wants to process or move (DDR, MIF etc.). We also disabled ATP in the end, but the errors were still there. But I'd say less errors were generated.
Because of that, my question now is the following: Is it possible, that the ATP is investigating these files and at the same time SCCM wants to process these files but is not able to (because sense (ATP) is blocking these files because it's investigating)? Due to that, SCCM is not able to move or process these files for the moment (even if it's only for 1ms) and generates an error because of this?