GA pilot reported a NMAC during approach to JZI non-towered airport requiring evasive action to avoid a possible collision.

Narrative

As I was approaching JZI for a full stop landing I made my initial CTAF call; 10 miles to the east going to enter the left downwind for Runway 09 from a 45°angle. Winds were 070/9 and ceiling was 7;000 ft. I heard another transmission of a general aviation aircraft taking off Runway 04; departing to the east. I proceeded to make another call that I will stay at 1;500 ft. MSL so the departing traffic can pass underneath us. I see the aircraft on ADS-B and notice it is continuing its climb to my altitude and heading towards me. I see on ADS-B what appears to be the aircraft turning to their left; so I make the decision to turn to my left to avoid conflict. I understand right turns are standard for traffic avoidance however in the moment I believed a left hand turn to be the best course of action for traffic avoidance. I did not get visual contact on aircraft until momentarily before the near miss. I did not hear another transmission from the departing runway traffic aside from their initial call and I made the mistake of assuming they heard our transmission and understood. My mistakes and course of action to prevent another incident as such. My mistake was I assumed that the aircraft knew our position and altitude and I continued on my entry to the downwind. My course of action in the future will be to immediately change course to avoid conflict in the chance the aircraft does not receive my position report.