NJ 2023 Tax - Part-year resident, Double-taxed income and low NJ tax credit

I (married, joint) am a part-year resident of CT and NJ, working in NY.

I received separate W-2 forms for federal, NY, CT, and NJ based on the days we stayed in CT and NJ (approx. 25%, 75%).  I also noticed NJ W-2 was slightly high, given that NJ did not deduct tax from retirement contributions (401k, ira,hsa). So, adding NJ and CT W-2 income surpassed the Federal and NY income. 

After preparing NY tax and getting the total tax and refund amount, I allocated 25% of the NY tax to CT and received some tax refund on the TurboTax online system as it should be.

For NJ tax, I was given 3 incomes (NY, CT, NJ all different numbers) and checked the NY and CT income boxes, so that I could only report the NJ income.

However, while preparing for NJ return, the double-taxed income was not automatically generated and I had to manually figure out the double-taxed portion of the NJ income: NY income / 75% = NJ double-taxed income, instead of NJ W-2 income which was higher. 

Example: W-2 NJ was $12000, but I calculate the double-taxed income based on NY W-2 $10000 x 75% = $7500 as double-taxed income. 

Also, no matter what numbers I entered here, I received lower tax credit from NY than I expected and the system showed I owed tax to NJ.

For example,

NY total tax: $1000

(My expectation) NJ tax credit: $750 (75%)

(TurboTax) NJ tax credit: $550 (55%), and tax owed to NJ: $100. 

Q1. Did I calculate the double-taxed income correctly? Or should I enter W-2 NJ income as is?

Q2. Why do I get this huge discrepancy in tax credit, and is there a way to correct it using online Turbotax?

Thank you for your time and help. Any advice will be greatly appreciated!