Minimal Fedora or something like LXQt and see if you can tolerate it.

Tbh any distro should be fine even the most bloated distro still lighter than Windows (use 1.5GB on average), if all you do is streaming 8gb should be more than enough

Not a full distro but perhaps take a look at the Games on Whales project?

You could do a minimal Arch install then it on top of that.
Or maybe since the whole setup will live on docker, maybe some flavor of immutable distro? I use and enjoy OpenSuse MicroOS

Install a clean Arch, then install Podman and run the wolf container. You will have everything needed in the containers. If you wish to play directly in your browser, run the moonlight-web container next to the wolf.

I feel like, as you already mentioned, a headless arch install sounds the closest to what you want.

I'm not sure why you need to write your own install script. What's wrong with the normal Arch install script? I've never used it myself, actually.

When I first installed arch, I wrote down each step in the tutorial video I watched into a set of discrete steps. I now have that .odt saved and can pull it up again whenever needed, so reinstalling arch isn't as daunting as it was for me originally, but I still have the flexibility of doing everything manually and understanding why I am doing each step.

Maybe MX Linux with Fluxbox?

Just see if you can tolerate Debian and lxqt before you start doing weird stuff.

What kind of weird mutant laptop is this? You may have more and cheaper upgrade options available than you think…

E: I found a couple of laptops that ship with that processor and gpu and they all seem to have two ram slots and ship one stick of ram in the 8gb configuration. A ram upgrade in that case would be $30 or so. Even if you needed to swap two sticks it would only be $50 to go to 16gb and help you a lot.

The ones I saw all had an nvme slot and a sata port with an ssd installed in one of em. I have had great luck speeding up slow ssds with spinrite running its level 3. I’ll spare you the explanation but it really works.

Be sure to allocate plenty of swap space