Well, I managed to get the Dashboard item back up via the first 5 bullet points of
https://buddypress.org/support/topic/missing-forums-directory/ .
But we’re still unable to render the actual forums anymore, e.g. from the forums’ “View” links, or /forums/forum. Just blank white pages, maybe the occasional 404. For that, we tried just moving to Mingle forum, but it doesn’t have subcategories (or even let you move forums between categories), so that’s a no-go. So, we’re still interested in fixing bbPress’s other issues…
Funny that. We got the same double-separation and missing menu on our end, but its the latest of our mysterious problems preventing rendering the forums on our website at all. (They used to work fine, but they first stopped showing on the site, then the menu too.) Disabling other plugins doesn’t fix this, apparently.