So, this is a special situation, as it was a scheduled payment under a contract with NYC, relating to a migrant housing program. The payment was made just before everything got DOGEd, and when DOGE found out, it lost its collective shit and forced the payment to be reversed.
However, all you really need to make a debit out of a bank account is a routing number, account number, and proper authorization.
DOGE can apparently manufacture authorization out of thin air. And I bet it has everyone's routing info and account information from everyone who has ever filed a return with the IRS and used Direct Deposit (or paid by check in the mail).
The payment was made just before everything got DOGEd
It was a valid payment, not made in error. They decided after the fact that they didn't like the valid payment, and reversed it. This likely involved fraud, because that's not a valid reason to reverse a payment.
The answer is, as always, "yes, as long as no one stops him".
At this point, Trump is simply saying "I will do this, this, and that", testing to see if anyone will say "no, you can't!"
The govt has always been able to garnish wages or sieze assets, yes, which is one of the intended upsides of a decentralized crypto currency (disregarding all of the downsides).