As of my knowledge firefox currently does not have built-in support for storing the primary password (previously known as the master password) using the freedesktop secret service DBus API or any other external password manager integration. Therefore, it is not possible to bypass the password prompt during startup or sync using these methods.
the purpose of the primary password feature in Firefox is to add an extra level of security by encrypting and safeguarding saved login credentials.
This is not meant to be stored or controlled by external password managers.
Firefox does provide some integration with external password managers to automatically fill login forms, it does not expand this integration to include the storage of the primary password.
The primary password is designed to be manually entered by the user whenever it is needed.