Illustrator/Photoshop freezes when saving any file during Time Machine "Concluding..." operations

Hi everyone, I have been having this issue for some months and it's becoming very frustrating.

When my Time Machine concludes, not always, but sometimes, if I save any Illustrator/Photoshop file during that time, the program suddenly stucks, the rainbow wheel appears and I cannot do anything except force exit.

If I retry in a while, nothing changes, it gets stuck again.

If I restart the Mac during this time, even the restart operation gets stuck, and the monitor freezes for several minutes before restarting.

This state of "paralysis" lasts for 10-20-30 minutes, this means that I cannot work during all this time, and it happens almost everyday, sometimes even twice per day. I think you can imagine how infuriating and time-wasting this issue is.

My technician suggested me to try formatting the external hard disk where TM is set; I did, it seemed to work for a pair of weeks, but now the problem is coming back more and more frequently.

The Mac is an iMac (Retina 5K, 27-inch, 2020), bought as new in summer 2023.

Can someone help me?