I had the exact same baloney happen to me on an old 2010 15" MBP.
The solution for me was to restart in safe mode (boot holding shift). That allowed me to log in without the log file display. I then launched MAS and saw that the update was still listed as available (i.e. it had not been properly installed), so I just selected to have it install again. After that it rebooted and resumed normal behavior. The update disappeared from MAS so obviously the second time around it installed ok.
I’m surprised that Apple a) doesn’t test these updates sufficiently before putting them into the wild and b) thinks that displaying a whole bunch of log files with no indication of what went wrong and zero instructions for the user on what they should do is in any way a good idea. It’s just Apple being sloppy. And it sucks. Hope you get your issue fixed. 