Just as an aside, in the UK, the Crown ie the government not the actual Queen, has first dibs on things that are deemed treasure trove (this find wouldn’t qualify, as the coins aren’t old enough). The finder gets paid the full value of the find as a reward if the Crown wants to keep it, and that is not taxable. If the find isn’t of great notability - no museum wants it, I guess - it gets given to the finder to do what they like with. Any subsequent sale by the finder may be subject to capital gains tax.
Is there any similar holdover in the US from the old “King owns everything” days, or has it moved on?