دَخَلَ الْمُشْرِفُ وَهُوَ يَحْمِلُ الْخَرِيطَةَ.
The supervisor entered while carrying the map.
دَخَلَ الْمُشْرِفُ وَحَمَلَ الْخَرِيطَةَ.
The supervisor entered and carried the map.
Wa-huwa yaḥmilu constitutes a nominal circumstantial clause: huwa is the subject, the finite verbal clause yaḥmilu is its predicate, and the whole clause describes the supervisor’s state upon entry. Wāw links the circumstance to its possessor.
The second expression coordinates an independent past verb. It does not, by itself, encode exactly the same simultaneous state.