Given that semicha died ~1600 years ago, where does this Sanhedrin get its authority from? Also, aren’t there very stringent requirements on who can be a priest? How do you know if someone is actually descended from Aaron and or Levi?
The messiah will probably sort out those questions.
None of us could ever know, but there are families who claim to have documented their lineage. In some ways you may not have to prove descent all the way, just prove a lineage to a known (or accepted) source. Doesn’t make it so but that’s one way to make the claim. And for the record this idea gives me the heebee geebies for probably some of the same reasons as you. Self-appointed people claiming all authority is ground zero for corruption, the kind of corruption that led to the destruction of the Temple twice before. Not that I really think they will get anywhere nor will they be widely accepted. But if some nitwit goes into the Dome Gold slicing up a goat in the name of God the mess he causes will be a lot bigger than any mop could clean.