I'd expect that every warrior puts in at least 40 hours a week, if not 60 or 80 or more, even in peace time, so they have to have something to do. A lot of it is training, drills, exercise, and so on to keep their readiness at maximum. But doubtless some if it is cleaning, some of it is book keeping, planning, and probably some of it is just make-work (though I've never been either in the military or even military adjacent, so that's more from fiction than fact).
But, as for MechWarriors, they're the feudal elite, so they probably put in their 40 hours very difrently. I often compare them to pro athelites, so one could imagine them doing things like looking over 'game tapes' (battle ROMs) of units they've faced or are about to face. Sure, some do work on their mechs, just as some race car drivers take an intrest in their cars, but others just trust it will get done, then drink a fusionare.
Conversely, in a down an out merc unit, much like a poor sports team or racing team, there's no ball boy, a minimum number of mechanics, and you do the work you need done yourself, for no overtime, because otherwise it won't get done. So you'll have warriors doing whatever they're good at, being medics or lawyers or techs or accountants or just helping sweep up. And, since many (most?) mech warriors won't be good at it, perhaps the jobs don't get done fully or correctly, and you suffer for it.
Lastly of course, in any unit officers do double duty as administrators and so on to some degree or another, but I don't think that's in question.