We are absolutely thinking about push notifications, the tricky thing is that we simply do not want to handle data for forums not hosted by us.
There are technical workarounds, we could say “Hey phone, site X wants you to refresh” this may work around the major limitation here. Maybe there is a way to encrypt payloads as well which can solve this.
These days PWA on iPhone (as long as you are not in Europe) and PWA on Android work quite well. But the Europe curveball makes us think a lot more about the app.