Do authentication in the reverse proxy if you can (e.g., basic auth or forward auth like Authelia, the second also has the benefit of SSO).

CAA can also be used to disable http verification, meaning you would have to have control of DNS to be able to get a certificate (which the VPS ideally wouldn’t have).

I use Caddy as a reverse proxy, but most of this should carry over to nginx. I used to use basic_auth at the proxy level, which worked fine(-ish) though it broke Kavita (because websockets don’t work with basic auth, go figure). I’ve since migrated to putting everything behind forward_auth/Authelia which is even more secure in some ways (2FA!) and even more painless, especially on my phone/tablet.

Sadly reverse proxy authentication doesn’t work with most apps (though it works with PWAs, even if they’re awkward about it sometimes), so I have an exception that allows Jellyfin through if it’s on a VPN/local network (I don’t have it installed on my phone anyway):

@notapp {
  not {
    header User-Agent *Jellyfin*
    remote_ip 192.160.0.0/24 192.168.1.0/24
  }
}
forward_auth @notapp authelia:9091 {
  uri /api/verify?rd=https://authelia.example
}

It’s nice being able to access everything from everywhere without needing to deal with VPNs on Android^ and not having to worry too much about security patching everything timely (just have to worry about Caddy + Authelia basically). Single sign on for those apps that support it is also a really nice touch.

^You can’t run multiple VPN tunnels at once without jailbreaking/rooting Android

Yup, there are many ways of doing that. Most reverse proxies should support basic auth (easy, but browser UX is terrible and it breaks websockets) or TLS client auth (even worse browser UX, phones are awful).

The best thing is do something like Caddy + Authelia (which is what I currently do with most things, with exceptions for specific user agents and IPs for apps that require it, aka non-browser stuff like Jellyfin),