Refactor DeprecationHandler to a standard PHPUnit extension

Problem/Motivation

Spin off of #3523614: [CI] Collect and report deprecation statistics and details.

The DeprecationHandler class was implemented as a replacement of Symfony's PHPUnit-bridge component, and uses initialization logic that is now outdated by more recent PHPUnit developments.

Proposed resolution

In this issue, we will

1. convert the DeprecationHandler class into a proper PHPUnit 'extension', using the bootstrap logic introduced in PHPUnit 10
2. introduce proper extension parameters in the phpunit.xml to configure the extension, and a new environment variable that could override the xml configuration at runtime in CI pipelines
3. make the legacy SYMFONY_DEPRECATION_HELPER variable redundant (still allowing its usage at least for now)

Remaining tasks

User interface changes

Introduced terminology

API changes

Data model changes

Release notes snippet