By default only the host of a meeting can record (afaik), so I'd presume it was the learning group staff.
No, anyone can record, although only the host can have it recorded and left on some US servers, but it's trivial for anyone to record.
This is one of the big problems with Zoom or anything similar, there are very good reasons to record it for safeguarding - protects the facilitator against claims against them, allows evidence and clarity if any of the kids ask for help etc. But obviously at the same time it prevents access for anyone who has any privacy doubts, or good reason to protect themselves.
A school saying "just don't attend if you don't agree" is extremely dubious, but then most of this is done on a balance of risks and rewards and whilst I would disagree with live video lessons entirely and slightly less disagree with video catch-ups. It absolutely depends on a balance of different risks and rewards for the activity.
For the facilitator wanting to protect themselves I can see a balance being on requiring recording (especially as anyone in the group can record anyway.)
Retaining the recording for any longer than necessary would be bad though, and storing it on zoom servers would be pretty silly, and you should have been informed, although of course maybe you were.
So YANBU to be uncomfortable, it's right to be, but equally a facilitator would be pretty Unreasonable not to record - it's all part of how shit doing stuff remote is.