Based on experience I would say they credit to 2025.

I say this because basically whatever date that the actual credit posts to their account is the date the bonus EQN states it’s in my account

Example -

Had a friend use a GOH for a Stay checking out November 7th. It posted to their account November 9th, on my account it shows under past activity November 9th 1 EQN earned, not November 7th.

I believe that Hyatt would have it this way as well since the expiration for them would be late February so a December 31st vs. a January 1st posting would make no difference to Hyatt as far as expiration.

Though this is the first year they’ve existed so not 100% sure if Hyatt has any special policies for year end posting of these bonus nights.