Q. Who determines if it is by convenience or required by work?
A. Your employer and eventually, if necessary, the NY tax authorities. If your employer is withholding NY state tax, he's already made that decision, under guidance from the New York Department of Taxation and Finance.
Your's is a common situation ("worked it out with my employer that I am not required to work in the office"). You moved to PA, for your convenience. So, you are subject to NY tax. A common example of "convenience of the employer" is that you have customers in PA that you need to meet with or your company has an facility there that you work in (an office with you as the only employee would not qualify unless you meet clients there).
Nobody has answered your question about NY CITY tax. I don't know the answer, for sure, but don't think you are subject to that, just NY state tax.
