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