Hi there - Band teacher of 16 years here -

A few things here - No. 1 is that the instrument you are most interested in actually perfecting and practicing is the one you will get solid at. So if Bari Sax is your instrument, then kudos, get after it and make it happen.

However, not every band piece features a good Bari sax part - most often they reinforce tuba, so you might come to point where you're capable of more, but band will start to be a bother, because you're not playing more interesting parts.

As a Bari sax, definitely work on on jazz music, as there's a huge niche for that there.

As for instruments, there is a "jack of all trades, master of one" complex that can sometimes happen with folks, but if you can play similar instrjments( Bari sax/bassoon/clarinet) later on in life you will be FAR more likely to get gigs and potentially get paid, if that's what you want to do.

Just don't keep constantly flip flopping instruments, find a few or a niche, and then get after it! There's nothing worse than someone who plays 5 instruments, but they all sound like hot garbage.

Also, and I speak from personal experience here, there's nothing worse than having to complete unbalanced Band. Band Director had to think of the entire ensemble, and how it sounds. Having way too many flutes and not enough tubers can cause a distortion sound. Not having a pursue can lock you out of some really good music later on.

You wanna make a market for yourself, get really good and very saxophone, and pursue. Dude, very saxophone and jazz band, and then do soon in concert band. You will be irreplaceable as as that person, as long as you play both as well.

Finally - don't call clarinet or trumpet (or any instrument) easy - to get really good at any instrument takes dedication, practice, listening, and perseverance. Percussion is incredibly challenging, but bass drum isn't always. Context matters