In MDL-83906 a PoC was created to reorganise the Backpack API classes within the core_badges component of Moodle, enhancing modularity and maintainability for future Open Badges (OB) specifications.
This issue should prepare this PoC for integrating it into the main codebase. Things to consider include:

• Implementing automated tests for the new classes to ensure their reliability and correctness.
• Deprecating any old classes or functions that are no longer needed (this can be handled in a separate issue if required, in order to keep the changes manageable).
• Checking coding styles to ensure that the new classes adhere to Moodle's coding standards.

This is basically a follow-up of MDL-83906 and should include changes made in commits 1&2 of the branch included there. The commit 3 (core_badges: Merge backpack-add and backpack-export) will be handled in a separate issue, in order to keep the changes manageable and focused on the reorganisation of the Backpack API classes.