in chrome (and edge for some reason) the url is
chrome-extension://extensionid
I use it to allow the add on to connect to my firebase, but i dont know the equivalent for firefox
Extension ID changes in Firefox with every install. And new Safari will change it with each run!
If you need string that won’t change, maybe hardcode one in your code?
If you need unique ID on each device, you can generate UUID and store it in browser.storage.local.