Yes the aux pressure relief button does shut the motor off as part of releaving pressure at the couplers.
You power problem is likely fuel related if the engine appears to be running normal under light loads. (no smoke, bad noises etc) Could be water has ruined the new filter already, the fuel lift pump is not working right. Try draining the filter and look for water or crude. if you find such, then new filter, maybe drain the tank. There is a cover underneath the rear of the machine held on by 3 bolts. The plug under the cover facing rear is the fuel tank, the one forward is the chain case oil.
If the filter looks good, have someone squeeze the primer bulb while the engines running to see if that improves its power (may not be easy to do if you have to work the machine to stall it out) but this duplicates the fuel lift pump and may rules it out.
How many hours on it?
Ken