Federal employee transfer to new job in different state

I live in Virginia. I worked for the federal government in DC in January 2023. In February, I started a new job which was a transfer to a different arm of the government which has it's offices in MD, (still a federal job and therefore a lot of admin was done via interdepartmental transfer). In my DC job, I always had VA taxes taken out and therefore only had to file VA state tax return due to reciprocity with DC. I did not realize, nor was I told by the new HR dept., I needed to fill out Form MD-507 so that VA taxes continued to be taken out of my pay instead of MD taxes once in the new job. Was this an oversight on my part or my employer's?

 

Further, I am doing my VA tax return just now realizing I only paid VA taxes in my previous job from January. Now I owe thousands to VA plus an underpayment penalty fee. It's asking me questions about AGI as of certain dates to help possibly reduce the penalty fee. I have no idea how to fill that out. It seems that is not even applicable to my situation (as I am a regular W-2 employee) and more for people who pay quarterly estimated taxes. Do I just bypass that question and forget about trying to reduce the penalty/ just pay it? I assume I am required to lay out the thousands due to VA plus the penalty ASAP (the penalty fee increases every day it isn't paid). Additionally, I must now file a non-resident MD tax return so I can hopefully get a full refund of MD state taxes from February through December.  How do I need to fill out the MD return in order to get this full refund; if I choose to add another state's return in TurboTax, will it auto-populate properly from my federal return information or do I need to adjust the income on the MD return to be $0? Will the VA state return automatically change in TurboTax based on my adding the non-resident MD return? Either way, I assume I will not be able to e-file the MD return as I need to attach an explanation causing the return to have to be physically mailed in, correct?