TA salary between different university departments
It's complicated and depends on a lot of power dynamics between and within departments. A few things that influence the system:

there is a correlation between research pay and TA pay for grad students. They are likely to be closer in departments where many grad students both teach and do research (no one wants their paycheck to vary wildly as they go back and forth)
having more grant money increases the options for how much to pay graduate students to do research.
paying grad students more money for research (and TAships if required) translates to being able to recruit better talent in some circumstances where grad students actually shop around for this (and aren't being wooed entirely on prestige).
competing with industry can influence the pay in a similar way, probably more in industry-adjacent fields. I wonder if in purple-collar fields like music it works against grad students, as people expect not to make money in the non-academic world.
TAs are cheaper than adjuncts who aren't enrolled, so departments that have a heavy teaching load like math have an incentive to recruit more TAs, and may raise their pay to do it.
professors in departments that bring in a lot of money either for research or for being a critical teaching hub have the power to push back against admin and fight for higher pay for TAs, if they choose to do so.
the administration of large universities have a huge incentive to keep TA pay low to save money, so that pushes in the opposite direction as above reasoning to increase pay.
unionizing (in my experience at the UCs) made the pay uniform across departments for teaching (though there were ways around it still) and it happened to be that the research assistant pay matched the TA pay and stayed pretty uniform.