I lived in 2 different states in 2023. Shouldn't my box 16 state wages for each state only show the wages earned during my time in each state not my total annual wages?

Yes, that is what they technically should show.  However, not all employers do it that way, especially if you did not report your move in enough time.  As you walk through the state returns, you will be able to adjust the income you earned in that state. 

Did you live in one state and work in another or did you work in the same state you lived the entire year?  

If you lived in a state with reciprocity with the state you were working in, then you would only have to pay taxes on the income for the state you were living in at the time.

If you lived in a state without reciprocity, and worked in one state while living in another state, then you would have to pay taxes on the income in the state you work in and the state you live in, getting  a credit for the taxes you paid to the nonresident state in most cases. 

Multiple States

File Non Resident State Return