I don't know that problem. Browsers should try to zoom everything proportionally, and I think they have gotten quite good at that (using Firefox almost exclusively).

Another thing that often annoys me is how sticky headers break text search. When you search and the browser scrolls just enough to get the hit "on the page", but still covered by the sticky header. The problem is: not using proper frames. Sticky covers part of the other frame. Bad.

Try looking at http://invisible-island.net/xterm/manpage/xterm.html on a phone. (Or maybe Firefox, too.) the side bar zooms too, covering page content, and if it's too big, it doesn't scroll.

Can't reproduce a problem with Firefox and don't have a phone handy. Maybe you can post a screenshot? The sidebar zooming too is what I would expect. At some insane zoom level the sidebar goes away, which is probably due to CSS and could be intended.

I don't see a sidebar covering content. Of course the sidebar takes some space, but as long as it's not over the content that's a different issue IMO.

This should no longer be the case, at least for Safari, Edge, and Chrome. All of these "detach" fixed/stick position elements from the viewport once you start zooming.