A330 pilot reported receiving an aircraft terrain alert during approach and executing a missed approach. Reporter stated the approach PAPI indicated well below approach path while the aircraft altimeter indicated on path.

Narrative

RNAV(GPS) Runway XX ZZZ. 1800 BKN 6SM. Followed OEM (Original Equipment Manufacturer) procedures in re-altimeter settings and calls at transition level; 10;000'; and on approach. Noted RA compared to Altimeter was at 2500 on first automated audible as well as at FAF and 1000' were consistent as a carry over from 5G AMOC (Alternate Means of Compliance) procedures however in review noted that the normal splits observed at those positions did not exist (first non-OEM procedure opportunity to trap an error in altimeter settings). The altimeter observation at FAF was exactly 2;300' as published. PAPI showed solidly 2-white/2-red. The outline of the hill was observable and the flight path trajectory appeared to clear the hill; however; the flight path angle seemed a little flat (second non-OEM procedure opportunity to trap an error in altimeter settings). Approaching the hill the PAPI trended toward 4-red but all electronic guidance appeared normal (third non-OEM procedure opportunity to trap an error in altimeter settings). Even when on the appropriate glide path; the PAPI in ZZZ is well known to show pink instead of white on a very consistent basis presumably due to refraction of the light due to moisture conditions; thus this non-normal PAPI presentation has become normalized. As we approached the ridge of the hill we received a GPWS alert TOO LOW TERRAIN and immediately executed a missed approach. Obtained a new updated METAR; corrected the BARO (barometric) settings; and executed another approach without further incident. Had we not executed the missed approach we likely would have crossed the top of the hill at 165' AGL however the actual minimum RA was not noted. The lowest RA I observed was above 300'.