An Instructor Pilot reported an NMAC when landing at a non-towered airport after they turned in front of a faster aircraft on short final.

Narrative

On the short final of Runway XX at ZZZ; I got very close to an aircraft that is conducting a missed approach to Runway XX because I misjudged their speed. There was also a confirmation bias on my side that created the situation. Below is the detailed explanation of the situation and corrective actions I should have taken. On downwind; I noticed the aircraft performing a RNAVXX approach into ZZZ by looking at the Foreflight traffic information. Then; right before I was abeam of the departure end of Runway XX; I heard the aircraft making a position call over the CTAF saying 'Aircraft Y; 5 miles final RNAVXX; low approach only.' With this information; I assumed that the aircraft is a single-engine aircraft and I presumed that they are shooting the LNAV approach; which was totally wrong. Then I checked their groundspeed via Foreflight and saw them flying around 105 kts.After getting the information; I was wondering whether I should extend downwind or start the base turn; then with my wrong assumption of his approach minimum; I decided to turn to the left base of Runway XX in front of the traffic because I thought there will be enough space between us. About 1.5 NM/1 minute horizontal separation when they execute missed approach. On the base leg; I had the aircraft in-sight; and the separation between us looked acceptable at the moment; so I decided to continue my landing. I could have gone around on the base leg and departed to the east at this point that would have eliminated the near-miss situation. During my final turn; the traffic also made a position call saying 'Aircraft Y; on 2 miles final Runway XX.' Therefore; I made a position call stating 'I am on short final Runway XX' in order to let them know I turned in front of them. I should have included the specific concern and said 'I am on short final Runway XX in front of Aircraft Y' so that the Pilot in the other aircraft is also alerted.On the short final; I was flying around 60 kts. ground speed; and I was expecting them to decelerate to 85 kts. ground speed and level off at LNAV minimum because I was presumed that they are doing LNAV approach. Then I saw the aircraft continuing to descend to the runway at a relatively faster speed. At this point; I finally recognized that my assumption was wrong and they are doing LPV approach to missed approach. I decided to continue my landing because I didn't want to penetrate their missed approach course and get closer while climbing each other. The aircraft executed a go-around right before the threshold; I am guessing at the LPV minimum; and departed to the north after that. There were many chances to confirm that the aircraft is performing missed approach at a higher minimum by asking on CTAF; executing go around earlier and depart the pattern; or changing my course of action to follow the traffic; however; I chose the worst option available for each decision making process and got close to the aircraft by misjudging their ground speed and presume their intention.