Recently I stumbled upon nb

It depends if your reverse proxy is inside your home network or outside. It should work without any other configuration if you forward ports 80&443 from external domain with something similar to rathole and configure reverse proxy inside home network.

This is not an answer to your question about using the same url, but see this article, it might be helpful. Tl;dr: mdns + reverse proxy.

What is the advantage of this extension over the bookmarklet? https://shaarli.readthedocs.io/en/master/Usage.html#adding-editing-shaares

I use mine as kitchen radio with https://moodeaudio.org/