I’m thinking a weekly recap per circle, sent by email. Would that be useful, or too much?

Yes, I'd use it. Per-cercle could get noisy if you're in a lot of them, so maybe one combined weekly email with a section per cercle and a setting to switch individual cercles off. Highlighting unanswered questions would be the most useful part.

One combined email with sections and per-circle controls sounds like a good balance if someone follows many circles. I agree that unanswered questions would be the most useful thing to surface.

If you build it, I'd put unanswered questions at the very top of the email with a one-click link to reply. That alone would probably get more questions answered than the rest of the recap.

Putting unanswered questions first and making the reply path obvious seems likely to turn the recap into a useful prompt, not just a digest. I’d keep the email short and let each person tune circles so it doesn’t become another inbox burden.