Well Im no expert but I am puzzled that the surface mounted brace survived all these years if it was left on since built as old as garage 'appears'. My first thought was someone added. I at least wouldnt be depending on the exterior let in brace shown (jeesh could they have cut the slots any bigger) going across 5 studs unless there was one in opposite corner same wall. Exterior siding, what ever it is (the stuff showing daylight between it and studs) doesnt appear to be doing much either. OP mentioned building was attached to another.
Its not that the external one should be there-it shouldn't, but I dont see much else doing its job.
If it were mine, simply an opinion, needed or not, code or not, I would block/sister the overly large cut-in slots. Never know, might want to hang your anvil from one of those 2x2s.
I would add fire blocking-not so much for fire (though OP said adding wiring etc) but tying the studs together for a bit more rigidity. Though shear panel would accomplish.
Lastly I would add the metal strapping mentioned, simpler, or trace and let-in the existing surface mounted brace. Again shear panels would accomplish. Might be overkill-might take half a day...But if just sheet rocking thats what Id do.
But Im neither an expert/carpenter/framer and have never stayed at the Holiday Inn.
My only other suggestions might be using green board at least on bottom-not seeing a lot keeping water out. And definatly use screws, hammering on those walls, either what you just nailed or exterior sideing could be issue.
If, as some noted, sill is NOT attached to floor, I cant see it, rent a gun and shoot it into concrete or bore and epoxy a few bolts.