Pilot reported an NMAC during final approach with a departing aircraft that was not communicating. Both aircraft took evasive action to avoid a collision.

Narrative

I departed ZZZ1 in a Cessna 172S direct ZZZ. Nearing the terminal environment at ZZZ I listened to the ATIS . It said landing and departing XX-XY; XZ-XA; XB-XC. I concluded I would request runway XB since I was approaching from the southwest; was familiar with the airport; knew runway six length and width was sufficient; it was suitable for the wind direction and velocity; and it was most efficient. Eight miles southwest of ZZZ I attempted contact with the tower and received no reply. I realized the tower did not open for another 7 minutes (XB:00 open and it was XA:53). I made three calls on the CTAF of my intention to land runway XB and I did so at intervals of five; three; and one mile. Before I made the CTAF call of being short final (one mile) for runway XB I heard Pilatus PC12 advise he was holding short runway XX. On frequency I thanked the Pilatus pilot for holding short and I continued to land. When I was about fifty feet AGL and nearly at the threshold for runway XB I observed the Pilatus PC12 begin takeoff on runway XX. The Pilatus pilot made no announcement on CTAF. This occurred just two minutes before tower opened (XA:58). I immediately executed go around procedures. I pitched for Vx to achieve the highest angle of climb possible (greatest altitude over distance) without stalling my aircraft. I was solo and lightly loaded so my ability to climb was decent for this type of basic general aviation aircraft. The intersection of runway XB occurs four thousand feet down runway XX. The Pilatus rotated before the runways intersected and was aimed directly up at my aircraft after rotation. Then I observed the Pilatus pilot pitch down and proceed runway heading under my aircraft. The Pilatus pilot never said anything on the radio. The controller in the tower; much to his credit; made an announcement of the Pilatus departing XX. I'm sure he made this announcement prior to the tower being officially opened because he was attempting to prevent a collision. I am not sure if he realized I was already going around but I was and I subsequently announced it on the CTAF. I did see the Pilatus rolling on runway XX a couple seconds before the controller announced it on the radio. I commend the controller's efforts and attention. I subsequently downloaded recordings and ADSB data for analysis. I determined separation was only 200' vertically. My ADSB track log makes very apparent I kept wings level until just before the intersection of runway XX so as to gain the most altitude possible but then steer away from the threat of the Pilatus. I also knew angling my wings might make me easier for him to see. All of my lights were already on for landing and my aircraft has upgraded LED lights. I subsequently circled and landed runway one-six without incident. The tower opened and the controller later (XB:13 hours) admitted on frequency reference the Pilatus pilot; 'He said he was going to hold short. I don't know why he started taking the runway.' On the recordings I was able to hear the Pilatus pilot transmitting on approach (north). He was not giving a full call sign. I subsequently determined the Pilatus went from ZZZ to ZZZ1. At the intersection of runway XX and XB Pilatus was going 108 knots and was 875ft MSL. At the intersection of runway XX and XB Aircraft X was going 61 knots and was 1075ft MSL (in a max go around climb). There was only 200' separation. ZZZ airport elevation is XXX' MSL. ADS-B exchange does not inherently correct pressure altitude for non-standard pressure. The pressure may have been 29.79 so if that is correct then altitudes are 130' lower. There was also an additional witness on the ground who observed the event unfold; spoke with me after my landing to confirm I was okay; and was greatly concerned about the potential mid-air collision due to the Pilatus pilot's actions.