Light aircraft pilot reported an NMAC on final approach to STJ airport.

Narrative

After calling St. Joseph Tower for a VFR arrival about 15 miles south; and about 2 miles in trail of another aircraft that we were knowingly following; STJ Tower gave us instructions to report a 3 mile final. Per the controllers own transmission; when aircraft #1 (we were following) was about a 6 mile final and we were an 8 mile final; I received a yellow traffic alert on my Aera 660 via ADS-B that there was conflicting traffic on a right base for the same Runway (35). The traffic was indicating 100 ft. below at the time; so I halted my descent to assess the situation and try to visually identify the traffic. Unable to find the traffic; and having not received spacing instructions from ATC; I initiated a climb as the aircraft appeared to be closing in on us (maybe 500-1;000 ft.) horizontally. My passenger spotted the aircraft right as it passed underneath us; making his final turn onto the final centerline. As the aircraft passed underneath us; the controller alerted the pilot to both of us currently on final and stated to make a 3 mile final and that he was #3 to land. It appeared the controller was not aware the aircraft was already on final and further out than 3 miles. I asked for clarification about the conflicting traffic and if they were on final; and the controller stated 'I believe they are below you; also on final and #2 for landing' which conflicted with his previous instruction. At this point I stated I would be performing a right 360 for spacing and the controller did not respond until about half way through my 360. The approach terminated safely; but we did see the aircraft pass below us by maybe 100 ft. after we were finally able to spot it. Considering I had climbed 200 ft.; it's entirely likely this would have resulted in a collision without an evasive maneuver on my part. The other pilot never reported us in sight.