TSA pre-check in STT exists in name only and is of little to no practical benefit. Maybe it has changed in the last 12 months but it is unlikely.

The water taxi will likely take you to Red Hook, possibly via St. John to clear customs depending on the recovery efforts. Figure on 45 minutes or so of travel time to Red Hook, add time for clearing customs (5 minutes to one hour depending on if there is a ferry ahead of you), and a 30 minute ride from Red Hook to the airport.. Optimistically you are there at 1:00 PM. Getting to the gate can take from 15 minutes to 2 hours depending on the length of the lines. Weekends tend to be busier than week days at the airport. If it were me, I'd reschedule the water taxi to 10:00 or take the ferry.