I think the issue is we still want it to be primarily desktop based - as Han says, BB forums are a dying breed, and the ideal 'modern' solution would be an alternative which is still desktop based but has a mobile form.

I've literally never used reddit in my life. Wouldn't know where to start with that one.

Discourse - can that be used on both mobile and desktop?

Discord, not Discourse (my bad). Yes, both mobile and desktop. I am told it works just like Slack, and Slack syncs very well across devices. I can ask my son, who is more familiar.

(EDIT)

Tried Discord from both my laptop and my Android phone, it works quite well for me, and syncs nicely. Completely forgot I had used it a couple of years ago for a forum I was briefly interested in. Also, looks like it is easy enough to set up a "server", the forum I joined is has multiple categories with multiple "channels" each, kind of like MF.)

Slack vs. Discord: Slack is more "private" (it is intended as a private forum for workgroups), while Discord is intended to be more "public" (meaning, it can be shared online). Both have ways to control membership. Both are free, but the free version of Slack only allows you to see the last 10k messages. The two UIs are similar, though I prefer Slack ("cleaner").

Discord originally started for "gamers" but has gained in popularity, with 56M users earlier this year (link)