PA-28 pilot reported a runway incursion and a conflict with an airplane on short final while taxiing to an intersecting runway. Reporter stated they thought the runway they were crossing was inactive and they did not see the landing traffic.

Narrative

At roughly XA:55 my PA-28 was leaving the ramp from the FBO at (ZZZ) after getting gas. After making a call to state my intentions to taxi from the FBO to Runway XX I quietly hear a long final call for Runway XX; although wind favored XY 'the adjacent runway' the traffic on long final gave me some form of assurance. (Pilots Note this was my first time ever at (ZZZ) I was unfamiliar and it was only used as a fuel stop so I had little briefing but when I diverted Center set me up for (Vis) XX. XX is also a longer and much more well kelp runway so there were multiple layers of assurance that XX was going to be the only one used. When coming up to the intersection of XY/XZ I stopped looking and made a call over the radio saying my intentions to cross what I thought at the time was an inactive runway. This was further assured as I could see the traffic on final for XX(landing light). I will note my glacé when I looked down Runway XY it was aimed down looking mostly at the runways surface and adjacent taxi ways. (In my mind no one would be approaching for this detection) so I did look up but I made no note of aircraft on final. I then proceeded to cross the runway looking mostly to my right looking for the landing traffic on XX. It wasn't till I was about half way across XY when I noticed a PA-28 touch down at the end of the runway and quickly take off. I the moment I realized the aircraft was there; I quickly added full power and got off the runway as soon as I could. I cleared safely and didn't see the aircraft even take off. Our distant over 500 ft. at all times but it definitely shook me up. I stayed on the taxi for a couple minutes just assessing what happen about 45 seconds later the landing traffic on XX landed safely. But the aircraft the did a Touch and Go called calmly said did you see me. I said not until you touched down and I did hear you either. I apologized for the situation and the Pilot said it's okay and he departed to the south. This is my best recollection. I will say this was my fault but I think the use of two intersecting runways less than a minute apart is also worrisome. I may have missed a call but the Pilot never only asked if he could see not hear so there's a chance a call was never made.