If you read the General Instructions for W2, you see the box 12 info and the HSA info.

You also see when this would not be in boxes 1 and 3, because it was done through a cafeteria plan, and when it is considered taxable and would have been reported in boxes 1 and 3. Then, you use the 1040 info to know if there is any portion that would be excluded under these conditions of not a cafeteria plan, exceeding limits, etc.

There is no One Answer. There is only what Applies to that specific facts and circumstances for this employer, their "plan" or not, that employee, the amount, etc.

If there is both employer and employee amounts, they are treated as the one total. There is no separation; it was contributed by or on behalf of the employee.