You can enter the number you entered for the Federal EIN or 999999999 for the State ID number. If the program won't accept that many numbers, just start shortening the entry (drop last number) until it does accept the number.
The state employer ID number is really only a bureaucratic convenience for your state's department of revenue; it's simply not an essential element to the correct filing and processing of a valid personal income tax return (either state or federal).
...OR...try leaving boxes 15, 16, 17 on the W-2 entirely blank.
All that TN income is GA-taxable anyhow.
A state ID number is only needed if State taxes wee withheld.......and TN doesn't tax wages.
Now if GA taxes were withheld for that W-2 , then a GA ID number would be required...