Multiple jobs: one in state of residence, one remote for employer based in another state

I currently reside and work a 9 to 5 job in Kentucky, but for 2022, I have picked up a second part-time, remote job in which the employer is based in Arizona. I am looking to verify the impact this may have on my tax situation.

 

I do not think I need to have any Arizona state tax withheld from my remote role pay, nor do I think I need to file an Arizona state return. But, should I update my W-4 for my 9 to 5 job in KY to withhold additional tax using the multiple jobs worksheet?

 

Please advise. Thanks in advance.