Is it normal for an agent to charge the buyer a separate fee after closing, on top of the seller-paid commission?

A fee you never agreed to in writing should not land on you after closing, so pull out your buyer-representation agreement before you pay anything. Since the NAR settlement, a buyer and their agent set the agent's compensation in writing at the start of the relationship. Whatever you pay your agent should be spelled out there. An extra fee is not automatically a scam. Some agents pass along a specific cost, like a transaction-coordinator fee or a technology fee, and a minority of contracts carry one. In a long career on the agent side, we have never charged a buyer a separate fee on a transaction, and we see it on fewer than one in ten contracts. We take the same view of junk line items on the mortgage side, like a small lender "technology fee." A business should absorb its own overhead instead of pushing it onto the borrower. So check the agreement. If the fee was disclosed and you signed off on it, that settles it. If it was not, ask the agent to point to exactly where you consented to the charge before you pay a dollar.