"If the company doesn't reimburse 2022 payments until 2023, what year would you add it to the W-2?"

2023.

As I noted previously, it follows the actual payment (cash basis), not the "premium period paid for" and you can see it in reverse.

If employees need to pay into a Sec 125 plan, let's say for Jan, but it is deducted from pay in Dec, that plan payment is part of the Dec year's W2 reporting, even if that is for a Jan premium to be paid by the employer in Jan.