This is the back of the top knob, which controls the direction of the output valve. If we can just change the knob and not touch/damage anything else that would be ideal since that'll be a bigger job
You’re already deep in to “bigger job” territory here.
Disclaimer: This forum is filled with people that DIY projects that even professionals will shy away from. And I’m one that will attempt pretty much any repair or upgrade, accepting that the deeper in to it I go, the bigger that repair gets. Not to dissuade you, but I’m not getting the sense that you’re as comfortable with tearing things apart by any means necessary and repairing or replacing whatever it is that isn’t working. Consider calling a plumber if you need to.
Ok, so … a quick google search didn’t turn up any jacuzzi diverter valves that look like yours. That doesn’t bode well for easy replacement if things go pear shaped here. But, inside that wall, you have a valve assembly something like this one:
Getting the knob off is needed just to get to the guts of the valve. A similar valve, exploded out, looks something like this:
With the knob off, you’ll have access to whatever retaining clips or similar that hold the guts in to the valve body. You’ll have to disassemble the valve body, where you will probable find that some kind of O ring or “rubber” washer has failed and will need to be replaced. You may, if you’re lucky, be able to buy the needed O ring, then reassemble the valve, and it works.
Or, you may need to replace the valve. Especially if you manage to damage it while attempting to remove the knob with that busted setscrew. Maybe you can find the manufacturer to get a replacement, but if it is indeed a cheep Chinese jacuzzi from a company that no longer exists, yo may have to adapt some similar valve in to the system.
If you’re really unlucky, you’ll also have to pull apart whatever wall this is all hiding in.