State tax filing

The same rules and filing are applicable whether you mail in or e-file your tax returns.  As @MarilynG1 states the information on your tax return is used to file the correct forms for the states; not the address on the W2.  What has passed has passed. The taxes have been paid (wrong state) or not paid (resident state) already.  Now you use your tax return to get a refund from the wrong state and pay the correct state.  

You are not going to get a corrected W2 due to an incorrect address that changes your tax return calculations. Unless the amounts you were paid (box 1) are changing, you do not need to wait for a corrected W2.     

However, you will need to submit a state W4 to have your employer change the state that it is withholding for going forward.

In the "My Info" section indicate the state you lived in on 31 Dec 2022 and use your current address.  This will generate the resident return forms for your resident state that does tax that income.  Since there was no withholding you will likely owe a tax to this state.    

Since you did not live or work in the state that taxes were withheld for,

1. In the "My Info" section scroll down to "Other State Income"  
2. Select "Yes" you earned money in another state  
3. Select that state from the dropdown menu 
4. Enter the W2 information just as your form indicates  
5. Go to the state interview and verify your nonresident status  
6. Continue to the "Income" section in that state return.  
7. There you will be able to enter zero for the income that should be allocated to the state. Your return will then show a refund of all the withholding entered from your W2.