As someone who has played piano for over 30 years and by any sane person's assessment I play at least "adequately", I can attest that worrying about how you play is the least constructive thing you can do and I have many times over my life crashed and burned when trying to play on the spot and in those moments people would question whether I knew how to play at all.
When I finally realised to stop caring (at least in the moment) everything got a lot better. Even if you screw up, owning it and laughing about it is better than curling up in fear and anxiety and making the moment worse and more awkward for everyone.
"stop caring" sounds like such unhelpful advice but when one finally realises you have agency over that, its like having a superpower