Not sure if this affects private islands like Castaway...The Bahamas just updated their travel requirements for vaccinated passengers:
https://www.bahamas.com/travelupdates
- Effective August 6, 2021, those travelling to The Bahamas from other countries who have been fully vaccinated will be required to obtain a negative COVID-19 test (either a Rapid Antigen Test or PCR), taken no more than five (5) days prior to the date of arrival in The Bahamas. The name and address of the lab where the test was performed must be clearly displayed on the test result.
https://www.bahamas.com/travelupdates