multiple instruments different key signatures?

Make sure you select the correct instruments when you set up the score and that you are viewing without the Concert pitch button selected (bottom right of window). When adding a key signature add it using the concert pitch definition. For your example you would need to add a two flat (Bb/Gmin) key signature. Musescore knows what transpositions each instrument works with and sorts out the correct key signatures in the score automatically.

See https://musescore.org/en/handbook/4/key-signatures#key-sig-transpose

You should read up on how to work with transposing instruments in the handbook:
https://musescore.org/en/handbook/4/transposition#transposing-instrumen…

The short explanation is that MuseScore supports two "views" of the score. "Concert Pitch" where all instruments are written "as sounding" with the same key signature, and "written pitch" where all instruments are written transposed as the player should read them, with different key signatures matching the instrument transposition.

And you can easily switch between them with by enabling/disabling a "Concert Pitch" button.