I don’t have a specific answer, but you could also look for tools that schedule reboots. If I remember correctly, a fresh boot has the same effects as lockdown mode. Fingerprint is not accepted, and the device contents remain encrypted until you unlock the first time.

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