[META] Reduce use of ContainerAware classes where possible

Problem/Motivation

In #3392616-5: Update to Symfony 6.4 we've found out that the Symfony\Component\DependencyInjection\ContainerAwareTrait and Symfony\Component\DependencyInjection\ContainerAwareInterface are being deprecated in Symfony 6.4.

Although we can't get rid off all implementations and will need to fork those into core, we want to get rid of as many usage as possible.

This issue exists as a META to group all removal of usage.

Steps to reproduce

Proposed resolution

Remaining tasks

User interface changes

API changes

Data model changes

Release notes snippet