UPDATE/SOLVED: it was not related to the music player, after all.
I had presumed that libmpg123 error meant it was related to my mpg123 background music player, but it seems that's may be not the case.
It only happen on "random video" screensaver mode, I am unable to reproduce on either "dim" or "slideshow" screensaver modes.
...and, it happens now even with the music disabled. Now mpg123 is still installed on my RPi4 but when disabled it is never brought up during autostart.sh so now is just ES(-dev), and my video files (mostly which come from ScreenScraper).
Looks libmpg123 is also used by the vlc (which I do use on ES, as I have "use OMX player for screensaver" set to "off.")
https://code.videolan.org/videolan/vlc/-/issues/1554
Seems it is caused by (one or more) particular video files. I (backed up and) deleted half my gamelists (so their videos won't be played), and the error still occurred. Then I restored my backups, and deleted the other half the gamelists -- this time no error! I have narrowed it down further to a single game in my SNES playlist -- confirmed by removing all other entries so only that one plays when triggering screensaver, and then the error happens right away.
I tracked it down to a single bad video from screenscraper. Whenever the Pop'n TwinBee (SNES) video is played, the Illegal Audio-MPEG-Header error is displayed in console, in multiple, when exit EmulationStation.
This is accompanied by a visual glitch in the video playback (or freeze, depending on player) at about 0:16 seconds in, just past the halfway-mark. This also was visible on the video served from the screenscraper website.
I tagged the video in a comment on screenscraper.fr asking to re- generate their standardized video. A short time later, that request was granted and, after re-scraping that one game, the error is now resolved!
For curiosity: if you have this game, and have a video scraped prior to a few hours ago (about 2024-03-22 19:00 GMT), do you experience the same console error after playing its video on screensaver and, after re-scraping, is it also now resolved?