Your move will be a qualifying event which will allow you to switch your ACA plan from a NJ ACA plan to a PA ACA plan mid-year. I think it's within 30 days or 60 days of the move, but don't quote me on that.
Your subsidies and cost sharing should be calculated based on your estimated 2021 income by both NJ and PA. Since the SLCSP will very likely be different between the two states, your subsidy will be different.
Your CSR should be "the same", because it's based on how your estimated income compares to the FPL. However, CSR is an actuarial concept, and how exactly the insurance plan that you choose implements it can vary from plan to plan.
I believe you'll need to start over on the deductible.
You'll of course get two 1095s in January 2022. You'll just combine these on your 8962 form by adding all of the numbers together on a month-by-month basis.
Some obvious things:
1. Make sure NJ knows you're leaving. Inform both your insurance carrier and your state exchange folks.
2. Make sure you don't have a gap in coverage. You should be able to end your NJ coverage at the end of the month and start the PA coverage on the first of the next. Contact both state exchanges to find out when to start the process on both ends.
My state has done weird things with my subsidy this year when I made some mid year changes. Basically their computers made some erroneous assumptions about the part of the year before the change. I don't think they're correct, but I can live with the errors and straighten it out a tax time. You might have to put in some extra effort with the PA folks to get the APTC correct, but since you're moving in the spring it probably won't be too bad if you have a problem at all.