If your doing this on a pi with raspian, both of these packages should be available. You can run sudo apt install cage cog in a terminal to install both of them.

I don’t know of an OS or distro dedicated to this, but it should be pretty easy using cage-kiosk, a window manager that only allows for a single window, and cog, a very basic web app container.

Install cage and cog on whatever distro you want, setup autologin, then in your ~/.profile add something like

cage -- /usr/bin/cog https://example.com

It should boot directly to the webpage at that point. Make sure to set up ssh before you do all this! System management might get tricky if you dont

Should note that Immich doesn’t have content provider support on Android, so you still need another gallery app to act as a file picker to select images in other apps. Other than that, I love it