moving expenses deductible after employer paid for part of the expenses; employer contribution was taxed

I changed employment in 2021 (filling after requesting an extension in April 2002).

My new employer reimbursed me for part of the moving costs (North Carolina - New York).

These reimbursements were listed as income on my W-2 and subsequently taxed, federal and state.

1) non-reimbursed moving costs can be fully deducted - correct ?

2) re the reimbursed costs that were subsequently taxed.  After tax, I had a net "in-your-pocket" amount from my new employer which was smaller than the gross amount which they initially forwarded to me.

Can I tax-deduct the difference gross-net of the moving costs that my employer covered  because the only thing that counts is the amount that has arrived at my end, to cover the costs of the move.

What did not get covered was out of my own pocket and thus deductible.  - Is my logic mistaken here ?