xscreensaver is controlled by xscreensaver-command. If xscreensaver-command is called with the argument -deactivate it behaves as if a key was pressed.
On my laptop running F37 that is happening every minute or so, so no screensaver. (F36 did not have the problem)
Replacing that command with a script that runs pstree shows
|-wpa_supplicant,952 -c /etc/wpa_supplicant/wpa_supplicant.conf -u -s `-xscreensaver-co,1119 /usr/bin/xscreensaver-command -deactivate `-pstree,1119 -agl
AFAIK there is no reason why wpa_supplicant should want to disable xscreensaver. I have two wifi networks, one local (not unusual) ans starlink.
Suggestions for additional investigation would be appreciated.