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.