If the server doesn’t process payments it should not cause admin a headache in most (?) jurisdictions.

It depends on how it works - if you just want a small ads type thing where you are allowing someone to say they have a thing and another person to contact them to say they want that thing, then they sort it out between themselves, that should be fine (NAL). You could, presumably, advertise services as well as goods. There were subs that kinda worked like this and there may be communities on here doing the same.

It would work nicely as a Fediverse service - you could post an ad and reply through an account on another service (the quality of your account could act like your reputation), boost it elsewhere (like Mastodon) to presumably like-minded people, etc.

Adding bidding might be a pain as the service would be locking in an individual's commitment to pay (as opposed to letting them sort that out between them).