for having recorded during a plenary session an interaction between a Member of the European Parliament and a member of the administration without their consent

Well, obviously, they are going to act to protect themselves. I don’t know the specifics of these cases, but these are public figures during a public session that was being recorded and the EU parliament makes those recordings publicly available. I don’t think there should be an expectation of privacy there. If you want a private conversation do it someplace else.

the President had decided to impose a penalty on Leila Chaibi for having recorded herself

Well, that makes the headline misleading. She was filming herself, I assume she had her own consent.