@zekuzelalem @fencepost I think you got this backwards: the authority in this case would be your (own) Mastodon/ActivityPub instance (which, at least for serious use, you might wanna trust, at least to some degree). The fishyness (phishiness?) of the “verification” site remains, anyhow.
For starters, in order to give evidence about my account being mine indeed I’d just publish a signed message that states this, e.g. using OpenPGP and by putting this info (or a link to it) into my profile description. In case the account becomes compromised I could at least revoke this statement (i.e. tell the world I got “hacked”), and should it ever happen that my crypto key gets into the wrong hands I’d, of course, have to revoke it in a similar fashion.
Yes, very technical, indeed, but maybe
keybase.io is more appealing to some (never have tried it myself).
Fun fact: all journalists at The Intercept (which, in general, delivers serious journalism – contrary to a lot of “mainstream” outlets) have a PGP key ready on their web site (which, I’m afraid to say, is all but standard among press and other entities).