Oh god, finally. A related bug, https://bugzilla.mozilla.org/show_bug.cgi?id=1569439 , was closed 9 months ago, and that made things slightly better (that one is about tooltips not disappearing when simply switching to another app), but I was incredibly disappointed to find that they'd still stay up when switching to another workspace.
On the downside, this is sorta a "wrong" fix. Tooltips should show up even if the window doesn't have focus (at least on Linux with GTK apps, which Firefox attempts to emulate). They should fix the actual underlying issue of them not disappearing when the mouse pointer isn't actually over the window anymore, when workspaces change.
On the downside, this is sorta a "wrong" fix. Tooltips should show up even if the window doesn't have focus (at least on Linux with GTK apps, which Firefox attempts to emulate). They should fix the actual underlying issue of them not disappearing when the mouse pointer isn't actually over the window anymore, when workspaces change.