Jellyfin runs locally, it's just accessible through a reverse proxy that I have running on the VPS. It's not really practical to run it on a VPS since hosted storage ends up being a lot more expensive and my library is relatively big. Bandwidth hasn't been a huge issue so far though as not too many people use Jellyfin at once. I could see it becoming a problem though if I hosted too many of the other services locally too, like Nextcloud, a Minecraft Server, Teamspeak (for some friends who are eternally stuck in the 2000s), gittea and several more.

I'd also need to run a second machine to host docker containers on or replace my NAS completely with something more powerful, which likely wouldn't make sense economically as I live in a place where electricity is relatively expensive.

I've got Jellyfin on a cheap ($20/year) VPS, and used SSHFS to attach it to some external hard drives attached to a Raspberry Pi. My upload speed is only 10 mbps, but that seems enough for most movies and TV shows, and multiple users can watch simultaneously via SyncPlay. Transcoding works too (up to 1080p)