I have just tried to disable every extension and it does not change anything
Should I have closed every google-chrome-beta window and re-open one to validate?
I have just (un-)toogled the extensions and try to open a new window. where others where already opened.
FYI, I have just applied some updates and rebooted the laptop.
It turns out that now, neither google-chrome nor google-chrome-beta has the window title bar buttons on the left side as configured in Gnome Tweak
After a quick check, google-chrome is now at version Version 107.0.5304.87 (Official Build) (64-bit) and google-chrome-beta is Version 108.0.5359.22 (Official Build) beta (64-bit).
Maybe it is something related to the Chromium >=107?