Can someone share some proof/a screenshot of Chrome or Edge offering you to install Youtube or, as @tigerknsoXIV stated, “any site” requested? I think it’s important to note that not every site can be added as an app/PWA.
On my end, I see sites like Community, Twitter, Pokedex.org, Soundslice, Medium, Pintrest, Spotify – all offering me the option to install at the top:
That’s on both Brave and Chrome. However, I do not see this option for all sites – namely, as @tigerknsoXIV mentioned in the OP, I do not see one for Youtube. And, logically, there should not be given that there is already an associated application for Youtube.