First of all, well done for getting to the interview stage and for approaching the interviews in the STAR format, reaching out to hiring managers proactively, and seeking to improve your interview habits.
What struck me was your question: Do I just pick out the ones that I think answer the panel’s question the best?
That's exactly what panels want, and cannot be stressed enough.
By the time you are at interview, they already think you may be appointable in principle. The interview is not about proving every good thing you have ever done. It is about answering the specific question asked, using the best evidence from your experience that match up with the job spec.
That becomes more important as you move into more senior roles as a key part of that is to convey complex information simply. Eg for some common behaviour questions:
If the question is about stakeholders, don’t tell the whole project story. Tell the stakeholder story. Who needed persuading? What was difficult? What did you do? What changed as a result?
If the question is about delivering at pace, focus on how you prioritised, what you dropped or escalated, what risks you managed, and how you still delivered.
If the question is about making an effective decision, focus on the evidence you weighed up, the options you considered, the trade-offs, and why your recommendation was the right one.
Importantly, if not already (your writing down the questions suggest you may not, but that may be unfair), instead of reacting to the question in the moment, try to anticipate them. It really helps to have a "gold-standard" answer ready for your motivation and why you're a great fit for the role. If you nail that first piece, you'll naturally relax into the rest of the interview. Similar to a previous poster, I suggest having a bank of "stump" answers for the main behaviours that tend to get asked for the roles you're interested in already written out and, crucially, spoken out loud several times. You don’t want to be wooden or sound like you're reading a script, but having that structure in your head means you don't have to scramble for evidence while the panel is watching you. And as others have also pointed out, of course be clear what you did and don't default to polite 'we'.
All that said, in my experience the single best thing to do in my experience is practice with a friendly, but frank, human. I appreciate that can be difficult and uncomfortable though, so hopefully the above helps!