I got other people on my network who prefer faster internet speeds over privacy, sadly. And I dont wanna be rude and just force them to do something they don’t want to do. (Even if it’s for the greater good)

This would not impact internet speed for anyone else on your network. Whether they're connected via Ethernet or WiFi, they'd have the same speeds as before.

As for a Wireguard connection tunnelling in from outside, it has so little overhead that it does not meaningfully impact speed or latency (I'd know, I use it every day).

Also, you can set up the tunnel as a split tunnel. This means that

• only traffic directed at your homeserver with the music server goes through the Wireguard tunnel while
• any traffic directed at the open internet does not go through Wireguard, i.e. zero speed or latency penalty.

Also attaching it to my router won’t work when I’m out travelling or away from home.

I'm not sure what you mean by "it" here. Feel free to fill in the blank.

Gluetun is a container to allow vpn connections. In docker any container you want to use the vpn connection you would put network_mode: service:gluetun and those containers would then use the vpn connection. With tailscale you would still access those containers through your tailscale ip address but they will be behind the gluetun vpn container. Tailscale doesnt act as a vpn as in masking your online activity it only secures your server from being accessed from outside of your tailnet. You can enable mullvad in tailscale but that provides mullvad exit nodes that any internet activity outside of your containers would be behind. Gluetun allows you to put your containers behind vpn as well. As far as speeds go, it might slow down abit but not much

No it has very little overhead. But you'll need to choose between tailscale of mullvad on your phone since you can't have two different VPN clients running at once on your phone.

Yes! I misspelled it :P