Remove proxy writer

[Zelldon]

Description

Removes the proxy writers, which have been introduced for not writing on reprocessing, which we no longer do.

Related issues

related to #9727

Definition of Done

Not all items need to be done depending on the issue and the pull request.

Code changes:

• The changes are backwards compatibility with previous versions
• If it fixes a bug then PRs are created to backport the fix to the last two minor versions. You can trigger a backport by assigning labels (e.g. backport stable/1.3) to the PR, in case that fails you need to create backports manually.

Testing:

• There are unit/integration tests that verify all acceptance criterias of the issue
• New tests are written to ensure backwards compatibility with further versions
• The behavior is tested manually
• The change has been verified by a QA run
• The impact of the changes is verified by a benchmark

Documentation:

• The documentation is updated (e.g. BPMN reference, configuration, examples, get-started guides, etc.)
• New content is added to the release announcement
• If the PR changes how BPMN processes are validated (e.g. support new BPMN element) then the Camunda modeling team should be informed to adjust the BPMN linting.

Please refer to our review guidelines.

[Zelldon]

Nevermind, we first need to make sure that the LogStream writer is no longer used in the engine and returns correctly a result then we can remove it.