I’ve been looking at VPNs, but it feels weird, to route everything through my home IP when I’m also trying to use a commercial VPN for privacy / to combat services fingerprinting me based on my IP.

My ASUS WRT router (running Merlin Firmware) forwards my Home WireGuard VPN server through one of my Proton VPN clients, I get all the added bonuses of being connected to my home network, utilizing my PiHole an such, while benefiting from appearing across the world.

I'm currently considering a reverse proxy setup with an authentication provider like authentik or authelia, but as far as I understand, that wouldn't work well with accessing services through an app on my mobile device (like for jellyfin music for example.)

This is correct, you cannot host an authentication service in front of Jellyfin’s proxy otherwise the Jellyfin Media Player will not connect to your server however, there is a Jellyfin SSO plugin for authentication which is what I use and I disabled the manual login form via CSS but be warned if you take this route that the CSS can be re-enabled on the login screen using your browsers element inspect, I wish you can disable it outright but it’s heavily baked into Jellyfin from what I’ve read.

I suggest setting up a IP-Blacklist for Jellyfin and only whitelisting the known IP’s.