M20J pilot reported remaining below assigned altitude to avoid conflicting traffic resulted in a NMAC event.

Narrative

APPROACH TO ZZZ. About 20 mi out ATC asked if I had weather and NOTAMs and my approach request. It was still a bit too far out to hear the AWOS so I asked if they could read me the weather and NOTAMs; they said no problem; standby. Meanwhile I still tried to pick up the weather using my second radio. Meanwhile they were giving me periodic step-downs for altitude to descend and maintain and one due to traffic at my 12 o'clock. Initially they set me to descend to 3000 ft. but changed their mind and said maintain 4000. I read back to confirm but neglected to change the altitude pre-select from 3000 back to 4000. I had noticed this a few hundred feet below 4000 and while correcting for this; I noticed unannounced traffic maybe 500 feet above me. Continuing to climb to 4000 would have put me closer to the traffic so I stayed where I was to keep an eye on traffic. At this time ATC called my call sign and asked how did I hear? They were a bit static and they were also busy; so there was a minute or so of making sure we could hear each other. Made me wonder if I had missed a call from them.