Update
I've gotten Rethink DNS working as best as I can tell
Mullvad via wireguard via RDNS is a little suboptimal because a lot of the servers are down at random times, so I am using the advanced proxy mode in order to have multiple mullvad servers as concurrent options so at least one is available at any given time.
Unfortunately, this means I can't let the DNS just take care of itself, I have to specify one. It freaks out if I try to enter the mullvad DNS into the AOSP Settings for Private DNS, so I am instead using DoH, specifying mullvad's DNS.
Weirdly, mullvad's connection checker says I am leaking DNS queries, but its only showing stuff that looks like mullvad servers. Not sure what that's about.
I've kept the app (not discord itself obviously) from talking to anyone but discord, which breaks notifications of course. I don't have play services installed anyway so that's kind of a moot point.
There's no easy way to get notifications without google, from what I can tell. Maybe the Vendetta fork "Bunny" might have something. Not sure.
Only other idea I have is to bridge discord to matrix and get notifications from matrix, but that sounds like a major pain.