General aviation pilot reported a near miss while taxiing to their cleared runway with an aircraft on short final approach to the same runway. The pilot stopped immediately; but was past the hold short line before doing so.

Narrative

I (Aircraft X) pulled up to the hold short line of runway 16 Right at HEF; holding short of 16R; and called Manassas Tower. I was promptly cleared for takeoff from 16R at XA15.As I taxied onto my runway for takeoff; I looked left to look for traffic on final and was surprised to see Aircraft Y; on short final. I immediately stopped my airplane but had already passed the hold short line. I inquired with the tower as to whether the aircraft was landing on my runway.I called tower; who informed me to hold position. I advised I was already past the hold short line. Tower then cleared Aircraft Y to land; just as Aircraft Y crossed the threshold of the runway. They had not been cleared to land prior to that. We were separated by max of 50-75 feet.The tower seemed to have lost track of Aircraft Y. Tower had been distracted by the report of a drone near Manassas airspace and was collecting information when I pulled up to the hold short line.Aircraft Y continued their approach and landed without regard to my presence. They should have gone around due to a fouled runway. They should not have proceeded that close to the runway without clearance. They should have inquired with tower about another airplane being cleared for takeoff from their runway.My looking left prior to entering the runway prevented a much larger problem. It was far too close of a call.