In February I booked two separate future stays at Hyatt properties.
They were prepaid, non-refundable stays. I used my Chase Hyatt card.
Total for both stays was about $10k charged to the card.
I am unable to keep the reservations and both hotels were kind to cancel the reservations and refund the full amounts to the credit card. This just happened today and the refund will not post for a few days.
You are sort of mixing apples and kumquats. Not saying it is impossible for Chase to pull points back, but, I have my doubts they easily can or will try unless they decide it was all a fraud. Meaning Chase bought the points and sent them to Hyatt on your behalf. That transaction is over and would require manual intervention to alter.
The one and only time I had a negative balance on my monthly credit card statement because of a big return they just ignored it. But I don't churn the card, I've had it for years, and it is regularly and heavily used. I was back to owing them money soon enough. Presuming yours is an active and well-used account I expect the same thing happens.
Finally, I had 2 stays and 10 nights credited to my account. Are these likely to get clawed back?
The spend bonuses? Same thought.
I would suggest you have an obligation not to abandon the card till it all evens out, but if you already had earned the first half spend bonus, and it sounds like you did some time ago, won't you be caught up and even soon enough? Beyond that keep using the card and don't worry about it unless it comes up. Which I doubt it does if you have regular spend continued over a reasonable time.
Presuming as I am that you are substantially younger that me, before I fly off in my annoying parental free-advice helicopter, please consider there is seldom a deal so much better that booking the no-cancellation rate makes sense. Maybe for a one-night mattress run to save status, but not a lengthy and expensive trip.