So a few things:
Firstly, this isn't really very similar to the style of John Williams at all. But of course, John Williams is an absolute master; he'd already been composing 40 years before his first film score. Writing a piece in his style is no small feat.
As for your mix issues, I'm not really hearing a problem with the overall levels on my end atm, but there are definite balance issues.
Some of these are due to musescore/musesounds which right now are notoriously unbalanced and have limited ways of fixing that, but some can't be. What you could do is put the tracks in logic and automate volume to help them out and send them in to a new reverb.
However, some of the other issues are related to orchestration and sample limitations.
For example, you have, as a lot of modern composers do, all these big block chords with a melody over them.
Bar 20 is a good example. Firstly, you have the trombones and celesta eating up a ton of the frequency spectrum by playing these huge chords, but then you ALSO have the trumpets coming in three-part harmony AND a String Melody in three octaves with the cellos taking the lowest octave. And everything there is playing mezzo piano. That's a recipe for mud, even in a live context I'm afraid.
Then, in bar 22 onward, you still have trombone footballs, but now they are accompanied by absolutely massive harp chords. While that is happening, you have different things happening between bassoons + horns, violins, etc. Another issue is that the bass is entirely footballs in the piece, which does not give it any breathing room and becomes rather exhausting to the ear.
"Melody + Chords" style Chord pads that have become popular in film music are actually generally considered bad practice not only because they're boring to play, but because the strings, low brass, and choir are basically the only ones good at playing them and these are large ensembles that take up tons of room in the frequency spectrum and stereo field. So you see beginners give this big, five-voice string harmony with a lonely oboe melody on top and then wonder why it's so hard to make the melody stand out even if the strings are at Piano. It's because the oboe is totally surrounded and your ear will focus on whatever line is thickest (the chords). If try to thicken the woodwind line, you're now competing for space with the strings.
However, unlike samples, live orchestras have almost infinite dynamic range, and not only that, but they can stay at one dynamic range and still have a lot of modulation in the sound, which is something samples can't do. So chord pads with samples tend to just sound bad. With these pads mocked up with samples, you're always going to fighting the fact that your chords seem like they just can't play quietly enough, and if they can, the timbre is bad because you can't modulate the sound without screwing up the dynamics.
TL;DR: You can fix some issues by loading it into a DAW, but the main problem is the writing/orchestration and samples suck at chord pads.