I was laid off for 90 days due to COVID and then notified it was permanent on July 1st--but now my employer is offering severance as

I'm in NJ and was laid off temporarily from Apr-Jul (layoffs due to COVID); the layoff was made permanent on July 1st. I was collecting unemployment during the temporary layoff, but now they are offering 20 wks severance (I had 20yrs in my position)--but only as continuation of pay. I have not accepted the offer yet.

I am confused as to whether I would continue to claim unemployment and file those severance payments as if I was working (and claim that I "worked") while those wages continue.

I also don't know how much extra severance taxes will be taken from those checks and am concerned it will be less than what I am getting on unemployment. I am also worried the severance will disqualify me from resuming to collect UI benefits when the severance ends (even though NJ has extended the UI benefits to an extra 33 weeks due to COVID).

Considering I'm over 50, need reasonable accommodations (such as remote work) and the fact my industry has frozen hiring, my greatest concern is that it will take a VERY long time to find new work--and I want to preserve the maximum amount time I can collect unemployment. I was thinking of rejecting the severance offer outright since I'm afraid it will impact my ability resume UI or get the UI extensions--and cant find any answers to those questions.

Will the severance payments, since they are continuation of pay, perhaps INCREASE my unemployment weeks available--as I assume they would have the appropriate wage deductions made for fed/state?

I'm trying to figure out whether accepting the severance will ruin any chances of collecting UI after the payments end and can't seem to find any way to know how much the extra taxes will impact those "continuation of pay" payments. And I still don't know how I would report the severance as continuation-of-pay on my NJUI claim, since it's being paid as if I worked/was on payroll (even though I didn't work for them since 4/2!)