I reproduced the issue with 6.02 and more patience, too, but it doesn't log anything. I locked the screen, and at 20:01 it spontaneously turned on again, and the XScreenSaver login screen appeared. At 20:15 I moved the mouse and unlocked (entering my password), and ran "xscreensaver-command -exit". Here's the full log file. It doesn't show any of the above described events.
########################################################################## xscreensaver: 19:30:12: logging to "logfile4" ########################################################################## XScreenSaver 6.02, released Oct 2021 Copyright © 1991-2021 by Jamie Zawinski <j...@jwz.org> xscreensaver-gfx: 19:49:43: screens in use: 2 xscreensaver-gfx: 19:49:43: 0/0: 1440x2560+0+0 (DP-1) xscreensaver-gfx: 19:49:43: 1/0: 1440x2560+1440+0 (DP-2)