Wrong state (NY) for W2

My wife and I are full-time residents of Indiana. I changed jobs last year and my new company is located in NY. I am in Sales and work remotely from my home/office (IN). Upon doing my 2021 taxes, I realized the State Code for my new company was listed as NY (Not IN). Since I waited to the last minute, my company could not send me a corrected W2 in time for my filing. I ended up filing my Federal and State (IN) taxes which included a several thousand dollar check for my income in which NY taxes were withheld and paid to NY instead of IN. This return was mailed on 04/18/2022.

 

Next, I went ahead and downloaded the NY state version of Turbotax and added it to the existing return (already in TurboTax, which included my Federal and State IN return) so the Federal Return Data would import (which it did). As it stands, the NY Return seems to be reflecting the proper amount that was paid to NY by mistake. The return includes forms IT203, IT203C, and IT-2. Since I did not e-file my Federal return, Turbotax will not let me file my NY State return so my plan is to mail it. Can someone tell me if this all sounds correct and if I'm over-simplifying or missing something? Thanks!