For implementing any type of marketplace, shop, etc., I'd recommend to run a self-hosted
BTCPay Server.
Bitcoin can definitely handle single-input, multiple-output transactions; that's actually the most common type of transaction, with the second output being change. I don't think that BTCPay Server or any other payment processor has a feature specifically for it though. So your best bet might be modifying
the code yourself.
The easier thing to do however, would most probably be to receive all the payments in your own wallet & then periodically paying out the recipients in batches. Since you can pay dozens of recipients with a single transaction, it won't add much cost overhead and would require no changes to BTCPay Server.