You absolutely CAN NOT log flight time as an SIC part 91 pilot, in an aircraft that is single pilot rated and the Captain is single pilot typed.
You are not a required flight crewmember.
PLEASE read the advisory circular on logging of flight time.
NO, you can not say you are required because the company requires it. This is a total myth, that the advisory circular is trying to clarify.
If you do it, you would have nothing but dual received added to your log book. That is useless and counter productive to your future.
If you receive benefit, and having your expenses paid, is a benefit, you need to have your commercial multi, or god help you when the FAA finds out.
It's not 1989 anymore🙄