Enable load balancing for WebHookWorker [RUN ALL RSPEC] [RUN AS-IF-FOSS]

What does this MR do?

We recently introduced the ability to use database read replicas in sidekiq workers, which relieves pressure on the primary. This is possible as long as workers do not issue any writes. This worker has been identified as a candidate.

The change is behind the load_balancing_for_web_hook_worker feature toggle: #331365 (closed)

Does this MR meet the acceptance criteria?

Conformity

• I have included a changelog entry, or it's not needed. (Does this MR need a changelog?)
• I have added/updated documentation, or it's not needed. (Is documentation required?)
• I have properly separated EE content from FOSS, or this MR is FOSS only. (Where should EE code go?)
• I have added information for database reviewers in the MR description, or it's not needed. (Does this MR have database related changes?)
• I have self-reviewed this MR per code review guidelines.
• This MR does not harm performance, or I have asked a reviewer to help assess the performance impact. (Merge request performance guidelines)
• I have followed the style guides.

Availability and Testing

• I have added/updated tests following the Testing Guide, or it's not needed. (Consider all test levels. See the Test Planning Process.)
• I have tested this MR in all supported browsers, or it's not needed.
• I have informed the Infrastructure department of a default or new setting change per definition of done, or it's not needed.

Related to #324376 (closed)