Is it possible that she just is overwhelmed by so MUCH activity and wants to sit it out because of that? Maybe she is telling you she is afraid she'll fail as a viable "excuse" to get out of it, bc if she says she's overwhelmed you might disallow her to do other things that she really DOES want to do. Or maybe she doesn't even understand that it is feeling overwhelmed to begin with, but she knows she isn't up for it for some reason.
Truly, without knowing the circumstances of whatever it is, and what her actual schedule looks like day in/day out, I'd be hesitant to push her to do whatever it is. Middle school can be a difficult time anyway. A lot changes and the kids are held accountable for a lot, and expected to be very independent all of a sudden. Some kids take to it wonderfully. Some kids do not. For some it's all overwhelming, just life and school, even without any extracurriculars.
I'd back off of whatever this is. She doesn't want to do it, mom. Don't make her. Choose your battles wisely. If she is as active and involved as you indicate (she does everything she can but is sometimes limited by cost, is what you indicate), then deciding not to compete/perform for this one thing isn't a big deal, except to you. It isn't to her, and that's obvious. She doesn't want to. Let her not.
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After your SWH:
I'm still not clear why you think she doesn't have any self confidence. It sounds like she does, but doesn't like you undermining it? I'm not clear what you are asking anymore. Are you asking how to get her to do this thing that she doesn't want to do? Or are you asking how to change yourself, so that you can be more supportive of her?
If the former, I don't think that you should. Let it go.
If the latter, then just drop all the "ifs" that you apparently pepper your "encouragement" with. She is old enough to understand that she might not win/get the part/be the best. Perhaps you are verbalizing all of that to prepare YOURSELF for the possibility that she might not be the top performer? She knows she might not win. She knows she might mess up. She knows that other people could be better than her. She does. So drop it already.
"Hey, so & so asked if you would consider doing x,y,z. What do you think?" And leave it at that. If she wants to do it, let her. If she doesn't, she'll find something else that floats her boat. Sounds like she is multi-talented. And that's great. But she really doesn't have to maximize her exposure to every single field she has a talent or interest in at this stage in her life. She can do one for awhile, and then do something else for awhile. It's one of the few perks of being a young teen. The rest of it can pretty much suck. So let her decide how and when she chooses to use her talents. And just ask her, don't try to soften the "blow" of "failure" before she's even tried.
The smartest people I know (and I know some extremely intelligent human beings) know that there is always someone smarter than they are. Pounding her over the head with that knowledge is not helping. So stop. She told you exactly what the problem is. Listen to her.