Restore from TimeMachine not working

This morning, my 2013 MacBook Pro (OS up to date) started to slow down without any obvious reason, and it stayed that way even after a restart. There was a root process running that was using around 70% of CPU time, so I decided to just go back to an earlier version of everything by using TimeMachine. Everything went ok (albeit verrry slowly, even the startup process), and I choose to erase the disk and replace it with a backup from a couple of days ago , since I hadn’t created any documents since then. It started up ok, but stopped at about 1.7 Gb copied. At that point, I could still consult the log file (it said ‘error while copying...) and choose abort, restart the computer and restart the process, this time with a different, slightly older back up file - same result: stopped at 1.7Gb, but now completely unresponsive, even the mouse pointer disappeared, I had to switch it off with a long press of the on/off button.

Now what would be the best next step?