Given the current times, I would definitely book direct. Things could improve a lot be September, or we could have a new wave of restrictions, etc. Booking direct usually gives you the most flexibility.

The one caveat--have you checked whether it is available via Amex Fine Hotels & Resorts? I had a good experience using that program last year. I was able to find a rate at FHR that was just slightly more than the standard rate, and I was able to pay at the time of the stay with my Aspire. This allowed me to get the additional FHR benefits (better than what I would have received as a Diamond member), while earning the full points as a Diamond (from the card, standard Hilton earnings, plus a bonus at the time), plus qualified me for a Waldorf/Conrad Amex offer (which brought the price down below the non FHR rate). Make sure to choose the option to pay at the hotel/resort.