'03 Protege5 Lurching/Rough Idle While Stopped w/ Brakes On

Hey all, I have an issue with my 2003 Protege5 that I need to get to the bottom of, while stopped/idling with brakes pushed in, my car is making irregular, small lurching/bucking or engine misfiring. It does not do this while idling in park and as soon as I accelerate it seems to go away and seems to shift fine, though the acceleration may just be masking it. It started on a very cold, snowy night. I am wondering if it is the timing belt or pulleys since I recently replaced the valve cover gasket because it was leaking and the timing cover had cracks in it and so I was concerned about the timing belt getting oil on it. Though from what I've read, power loss is a more common symptom of this and I don't think I've experienced any of that. The car is at about 137000 miles and I bought it at 130000 and do not know if the original belt has been replaced. Could it instead be due to an exhaust leak or bad o2 sensors? Thanks for your input.

Could be something as simple as a dirty MAFS, remove and clean with CRC MAFS Cleaner and reset ECU.

Youve got an Automatic right? Whats your idle speed at? Is it throwing any codes?