Oh yes this helps heaps!!!!! thank you so much! There's an important detail I wouldn't have known about otherwise - your model's missing its battery cover!
Batteries in connection models can be fiddly - if they're just a little bit loose, they'll freeze the device (which is probably why you're able to get to that download/reset screen before it freezes). Sometimes this happens with my V6 - having the cover basically negates the issue because the battery's got nowhere else to go.
My guess is that your cover's long gone by now, which
sucks because getting replacement covers for these is a pain. "buy a new tamagotchi and use that one's back plate" sort of pain LOL. if it makes it any better, any connection-era cover (V1-V6!) will likely fit on the back of that model. You could possibly go around this by using something to stick the battery in (tape over the battery/tape something over the back to hold said battery down), and then test it from there. Other than that, your Music Star is actually in fantastic condition! You've taken great care of it for sure
(doesn't even look like it's ever been dropped... gazes at mine with envy BJDSVBJD) Those buttons don't look worn out to me at all and sound like they're squishing nicely, which is always a good sign.
If it does end up being the buttons that's the problem..... I'll see if I can seek out some tutorials for opening up a 'gotchi, they're universal for all connection-era models - so if there's a tutorial along the likes on how to open your V3, it'll work for yours! it's very convenient actually bdksjvbdfjv
EDIT:
Found an eBay listing that sells 3D-printed backplates! I'm assuming yours is a North American model (the screw placement matches with the listing's demonstrations!), which means these'll fit yours perfectly. If it comes to this, hopefully this'll be of some help!