This is a challenging and anxious situation.
My personal experiences in similar scenarios at non-controlled airfields along with feedback afterwards from extremely experienced pilots.
The other aircraft may provide a very incorrect position report. I have joined circuit downwind with another aircraft clearly transmitting they were entering, backtracking, lining up and rolling on the opposing runway with no aircraft to be seen on the strip the entire time and no response to four repeated queries of their position until I called late final with a very heightened preparedness to bank hard right and power on, only to see them 50m off my port 10 o'clock at equal 150' flying the opposite direction in a twin. This was a new and very unsettling experience.
Advice received for above was: "If the other aircraft is not visual where they say they are, request they "CallSign" confirm they "are" where they say they are and to acknowledge your request", and be prepared to exit the circuit immediately if you believe it is required.
Runway numbers can be misleading if either aircraft has them perceived in reverse. (I have done this, and safely exited the circuit as soon as I realised the loss of situational awareness early in the circuit).
If one aircraft is familiar then that's still 50% chance of something going pear shaped. Get familiar, and if the other aircraft is clearly not situationally aligned then use the radio to advise; that's what the radio is there for.
The radio is not there to abuse other aircraft in flight for making an error. You can do that later on the ground when it's safe to do so if you feel, or submit an incident report.
Primary objective is to fly the plane in a safe and responsible manner.
Learn from every flight.