By policy Hyatt goes to the following year, ie check-in Dec 22, 2020 checkout Jan 9, 2021 the nights go to 2021. So this year if you register for promo and check out by Jan 4 you'll get double nights for 2021.

I'm thinking of booking an extended Dec checking out Jan 4 stay just for the 2021 Globalist re-qualification if it doesn't seem Hyatt will ease status requirements. I might just book a category 1 near my house for this as rates so low its worth it

Starwood was different on Jan 1 crossovers. I don't know what Marriott is like.