If you use the browser extension on Firefox it will do this automatically.

You’re correct. The Fire Stick would be a client. I currently use a Pi 4 as my server and it works great, but I use KODI instead of jellyfin. This means that nothing trys to transcode when I use it. However, my brother is able to connect to my server through Tailscale and he does some sort of GPU pass thru with a jellyfin container and as far as I know it works great.

If you’re looking for mini PC recommendations, I have been very happy with my Beelink Ser8. It was chosen specifically for handbrake encoding and is an order of magnitude faster than my underpowered decade old desktop.

Edit. I just reread your post saying that you don’t want to buy a mini PC so disregard that advice but if you want to stream to TVs on a budget, I am a big fan of the Fire Stick. If you get them on sale, they’re usually available for half the listed price (about $25 when I got them). You can get them on ebay if you don’t want to support Bozos. Currently they’re very easy to configure and they work great as long as you can get over the clunky menu design.

You may want to check out https://www.thewebernets.com/ blog posts. I use some of the recommend setups for my movies and most look great, but I do use subtitles which I think he mostly skips in his setups.

I am just some rando but I think this poster may have meant tinymediamanager as opposed to tinymusicmanager. I use tinymediamanager and it’s great.

You could probably name any race from Trek and justify them as Gorn food.