Couple of thoughts…
There are browser extensions for this! OGS users have used stylish to mod their boards before that was supported natively: How to customize boards for each tournament/ladder/game
It actually is auto-sized to 25% of the screen (see flex-basis
in the css). 340 px
is just the min width.
Finally a visual warning about the suggested change:
iPhone SE2, chat set to 500px