I'm looking forward to the answers you get because I've wondered the same thing.

The only hardscaping I want to do in my garden is a recessed circular area, same size, maybe a little deeper. I believe in my climate and soil, it will 100% need a piped drainage.

I cannot really avise what to do but you will need drainage and all planned before anything else is done. I have used what looks likedry river in some lansdcaping but to have a seating area there will require huge work to keep water out of the actual house . French drains work but require proper slope and a good contractor and a big mess . Post a picture that never hurts . This a nice sied space so you want to be able to use it so IMO worth doing it right

A french drain is not what you want for the patio itself. In order to work, it has to collect water after it has entered the ground. That is not sufficient under a patio. Though, one should be placed at the perimeter base of the retaining wall to lessen the water coming in to the recessed area and not have hydrostatic pressure affect the wall.

If your "circle" is wholly recessed (meaning no open portion with walkout at grade), then I would suggest a floor drain with the circle sloped towards it. A floor drain would be a catch basin. Then you would run rigid Sewer&Drain pipe from the catch basin to the gravity-sloped discharge area.

Thanks so much, a contractor suggested the catch basin and we were trying to figure out how that would work to the sloped area. Appreciate the info!

I would talk to at least three contractors beore making a decision.