I think it'll depend a bunch on what's getting cut.
Right now, I imagine the biggest immediate impact would be security on maritime shipping routes. Countries will get mad because the trade lanes are getting more risky/expensive. They'll probably step up their own efforts to police the high seas.
Secondarily, I imagine Israel and Taiwan will be the most impacted. They'll probably be scrambling to look for allies and defense agreements from other countries.
On average, does this cause other countries to start spending more on their military? Or does it make them go "oh, the US is spending less, therefore we should too"?
does this cause other countries to start spending more on their military?
They will, but I think that this isn't the issue.
The issue is that the US will be saving dollars, which could be infinitely printed (at least until recently), at the cost of goodwill and influence, neither of which can be printed.
I think a drastic reduction in personnel/bases/equipment if it was done too quickly could be very destabilizing. While I don't like America policing the world, that is the current state of affairs and changing that abruptly could be dangerous.
Cutting expenses by 50% would also be a big change and likely affect some personnel/bases/equipment but also likely cut out a lot of waste and grift. I am not sure you could do it without affecting veterans benefits though which will be immensely politically unpopular.
There would be significant ramp ups in military spending then, with the removal of military bases from foreign countries. There's been a deal in place (implicitly for the most part) that America will provide defense if those countries play ball and use dollars.
It would save Americans a ton of money and be better for hundreds of thousands of military families. I doubt the concessions we're currently getting benefit normal Americans much, but they're great for the regime.
Assuming we're also including the CIA and other covert meddling, I think we'll discover that a lot of global conflict has been a creation of the American regime.