Just for completeness there was a web+mastodon URI scheme in the use years ago but it got removed: https://github.com/mastodon/mastodon/issues/6255
The tl;dr is that URI schemes have bad fallbacks on the web. If the user doesn’t have an app installed then either the browser doesn’t do anything (it’s bad), shows error page (worse) or a chooser (which, in case of no app installed, also doesn’t help).
acct URI scheme is internally used by WebFinger if someone searches for accounts using the @account@example.com text.
Sorry for not offering anything actionable 😓