Moved to TX over 2 years ago from AL but haven't changed residency yet, can I file as TX resident for 2023?

For income tax purposes, you are a TX resident.  You do not need to file an AL return unless you have some AL source income, e.g. rental property. Then you would file a non resident AL return.

If you moved to TX in 2021, you should have filed an AL part year resident return for 2021 and should not have filed a 2022 AL return, at all (unless you have some AL source income).

TX does not have a state income tax.

If you did not live or work in AL you do not need to file an AL tax return, unless you have some other income that you are receiving from AL.     And....TX has no state income tax.   You file a federal return, and you use your TX address on it so that the IRS has the correct address to use if they need to mail you a letter or a check.

As for your driver's license, etc.---you need to find out what the TX laws are regarding that, since it seems that you now live in TX and should comply with the laws in the state you live in.

https://www.dps.texas.gov/section/driver-license/driver-license-services-appointments