Remove usage of WriteCheckSessionHandler

Problem/Motivation

Part of #2959269: [meta] Core should not trigger deprecated code except in tests and during updates.

This is another one that seems to be reported on every request, so also setting the priority to major.

Need to see what exactly we need to do, just removing the proxy class resolves it, wondering if we have test coverage for that lazy writing, I hope so...

Proposed resolution

• Merge functionality into \Drupal\Core\Session\WriteSafeSessionHandler / session_handler.write_safe service
• Remove session_handler.write_check service
• Open follow-up to use built-in PHP functionality - [#3001185]

Remaining tasks

User interface changes

None

API changes

session_handler.write_check service is removed

Data model changes

None

Release notes snippet

The service session_handler.write_check has been removed from core.services.yml. In the unlikely event that this service is being swapped out the functionality has been moved to \Drupal\Core\Session\WriteSafeSessionHandler - the session_handler.write_safe service.