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twocats just get out and play in front of people more
Truth be told, that's basically it. There is a reason why theatre companies have dress rehearsals where they try to emulate the real thing as closely as possible. We're all dogs But that's not helpful, I know.
I don't have any helpful tips to cope with the different environment (lights, other piano etc), and I know you said the people don't bother you all that much. But here's hopefully a helpful tip for people who do fear the crowds: humanize your audience. Don't just think of them as a sea of faceless monsters waiting to laugh maniacally at every one of your mistakes, but think of them as your friends, people who are rooting for you to do well. If you can, look at individuals (not too long, that'll get the person uncomfortable), but just briefly look them straight in the eyes (people love interaction and to get acknowledged) and then imagine a brief detail about them. Such as:
That man is twitching his nose, probably because he is trying not to sneeze while the person before me is playing, that's so considerate of him! (then you can give him a playful wink) Or that woman looks a bit sleepy, I wonder if she has insomnia like me/my spouse/my friend. (you might even be able to provide a friendly smile) Or even oh boy, that dress makes her look like a blimp! (try not to giggle).
People visit recitals to have a good time, literally no one is there to hope for a mistake to happen... and if (when) that happens anyway, they all feel bad for you. And if you manage to laugh/smile/shake it off, they'll be relieved with you - because if it didn't bother you, it won't bother them. Being uptight rubs off, and it makes people feel uncomfortable. But the good news is that feeling relaxed rubs off too, so if you can pull that off, you're looking at a sea of tranquility. That's why most entertainers learn to mask their mistakes with a quick joke at their own expense