Does abandoning prolongation in prayer for fear of showing off invalidate it and necessitate its repetition? And how is sincerity achieved?

You must not be concerned with who is or is not present among people during prayer. You should pray as usual without being bothered by their presence, and you should only be concerned with Allah Almighty's gaze. Therefore, do not shorten or lengthen the prayer for the sake of people. If you were to shorten it for fear of showing off (riya'), your prayer would not be invalidated, but you should not abandon a good deed for fear of riya'. You should also abandon obsessive thoughts in this regard.