I've just had one of these competence-based interviews. I'm the same as you - a bumbling nervous (embarrassing) mess.
I did some practice beforehand - especially for the work-based scenarios - but I really struggled to think of examples. I also purchased InterviewGold. It helped calm me down as I found the competency/strength-based model overwhelming to get to grips with, at first.
I thought my competence-based interview went pretty badly (said some stupid, irrelevant things but I was enthusiastic) and I had to keep asking them to repeat the question halfway through because I couldn't remember what I was answering 😬😂
The second interview was much more informal.
After just two interviews I'd totally had enough - it was sooooooo stressful and I didn't feel I could keep on with it. I didn't think I'd ever get a job and started to feel pretty bad.
Luckily (and amazingly) I was offered both jobs.
I got feedback from the competence-based one and, as I thought, I didn't score very highly (but enough), so not sure how I got that one.
The example questions usually fall into a few simple categories (conflict with someone, helping someone, how you solved a problem, etc.) so think about your examples beforehand (and think through each step of the solution, especially the outcome and what you learned). Also, it's good to use the STAR approach (Situation, Task, Action, Result but concentrate on the Action and Result) to help keep you focused.
Good luck... x