After checking Apple’s documentation, your understanding is essentially correct: Safari’s page-zoom settings do not enlarge the Safari menu bar or all of its built-in interface text. Apple provides separate controls for those areas, but they are limited.
On your MacBook Air running macOS Monterey 12.7, check Apple >> System Preferences >> Accessibility >> Display.
If your version shows Menu Bar Size, choose Large and then log out and back in.
Apple specifically says that logging out and back in is required for the change to appear. (Apple Support)
If you have already done that and the Apple/File/Edit/Help text is still too small, Monterey does not provide a further setting to choose an arbitrary font size for those menus.
The general text-size controls apply only to compatible apps and system features. (Apple Support)
The same distinction applies to Safari. Safari's Command + or Page Zoom settings enlarge the contents of webpages; they do not provide a corresponding control for Safari's menus or every part of its Bookmarks interface. (Apple Support)
So, given everything you have already tried, I would agree that there is not a normal Monterey setting that will make all of those tiny built-in Apple/Safari interface fonts substantially larger without also enlarging other parts of the display.
