PTO Cash out upon resignation

A PTO Cash out opportunity was given as my previous employer. I was assured by my manager that this would be paid out even though I was leaving the company. The information given by the company was vague and open to interpretation. The specific section states "You must be actively employed at time of payout to be eligible for the cash out payment. The PTO cash out payment will be made on October 16. Once you submit you request, changes cannot be made." This was interpreted by myself and others that you must be employed at the time of the election period or at the end of the pay period. However, HR is stating that I had to be employed at the time of the payment. Since this uses two different terms "payout" and "payment" there was the assumption that these were two different periods. At this point HR has only replied to me stating "you must be actively employed at the time of payout" but with the differentiation in the terms and their definitions this is true. I was employed at the time of the payout period.

Ultimately I made an agreement with my manager that I could stay an extra two weeks if the PTO cash out would still pull because it made up the difference between me current vs new salary. I was assured this would still pull and have explained all of that to HR, but now HR is not providing me with a response.

Important dates:
09/16-25 : Election period
09/23 : Cash out election made/ confirmation received
09/27-10/10 : pay period associated with PTO cash out payment
10/16 : Final paycheck