This usually affects users who originally purchased the standard version of the game before choosing to upgrade.
Please try deleting and redownloading your copy of Sea of Thieves - this usually solves the issue.
Other steps to try:
- Enter the Home Base
- Highlight Sea of Thieves Beta and select 'View Product'
- Select the Ellipsis (3 dots)
- Select your newly purchased edition from the drop down menu
- When viewing the different logos, select the logo without BETA in the image
- Game should begin downloading
If the issue persists, please reach out to https://www.playstation.com/support/ where they will be able to review your account and make further recommendations.