I wouldn’t say it’s unmusical, but there is very different technique from classical singing to musical theatre singing, just like there is again to various kinds of pop singing.
I grew up classically trained and went into MT from that and it was a significant benefit. Many of my peers didn’t have sight reading skills and struggled with musical notation because they trained with lyric sheets and listening to recordings or a teacher and just singing back. My DS does musicals and has gone down a similar path - he has his more classical lessons privately and then also does group lessons through a stage school. At 10 he is preferring any opportunity to actually have the sheet music for learning, and it has put him in a much better position working shows now, as rehearsals take much longer when someone can’t sight read.
MT is chock full of belting and it takes some adjusting to hearing it so much tbh! But pitch should be accurate… the oddity does come that in some styles of MT, a lot of riffing is encouraged, and that can do all sorts to the pitch, which may or may not actually sound great in the end. Not all MT is this way at all though, and there are a great many shows that require cast to sing exactly what is written. There are even a handful of parts that tend to use more classical technique for sopranos, though they are more the exception than the rule.
Honestly I would encourage the classical training as long as possible, even alongside any MT lessons or school. It will only help and she will be able to adapt and go back and forth. Classical training will help her more with range and breathing too, most likely, so all a plus.
All that said, if you can’t stand to listen to it, maybe see if you can steer her away! ;-) But there is quite a wide variety of style in MT so maybe all will be okay really. :)
I do find the sound recording quality on TikTok can be absolutely rubbish too, fwiw.