ShiroKuro what an interesting read! Thanks for sharing. Anecdotally, I tend to smile when I make a mistake (I can't really laugh out loud at myself during the performance, after all), and it does always seem like general audience members don't notice or care about my mistakes as much as a result. And I believe there is definitely some truth to the impact of a person's framing on their subsequent performance. "I can't do X" becomes a self-fulfilling prophecy, as does "I haven't done X yet but I can/will".
Where I fall on a lot of these things (how to bow, expressions while playing, etc.) is "it might not help, but at the very least it won't hurt!". Once when I protested to my teacher that I have RBF when I play and that any smile during a particularly spritely piece would be fake, they replied, "If it's genuine, that's even better! But your audience will enjoy what you think is a fake smile more than a frown!" Another way to think about it is, your appearance/mannerisms/behavior should at least not detract from your playing (above that threshold, people generally don't care).
Somewhat related, it definitely feels like practicing to perform is a distinct activity from practicing to learn. When practicing to learn/refine a piece, it's often good to tolerate no mistakes - if you make a mistake, stop and practice until it's fixed, otherwise you're basically practicing the act of making mistakes. On the other hand, stopping at every mistake while practicing is, well, practicing the act of stopping whenever you make a mistake, which is the last thing you want to do in an actual performance.