How to use it for a different web site?
More details about that on their github page [1]. It seems you basically need to include a JS file from [their CDN](//cdn.jsdelivr.net/npm/eruda).
As someone who fondly remembers the early Firebug days, it is great to see this. It is very frustrating to me that tablets and phones are so powerful, but we can't do even basic dev stuff on them.