PA resident has all wages taxed in PA. PA wages are typically higher than federal wages since retirement deferrals are taxed as wages in PA.

PA resident has zero NJ wages, even if worked 100% in NJ. If NJ employer refuses to withhold PA taxes, and they can, then TP has to pay PA estimates.

All NJ tax withheld needs a NJ NR return to get back the NJ tax. You should attach a copy of PA to prove it to NJ.

You CANNOT get tax credits from other jurisdictions for NJ tax nor PA tax, since it is illegal for NJ tax to be owed by PA resident who is a NJ employee.