Deprecate `LoadBalancer#select_caught_up_hosts`

What does this MR do?

Implements #335107 (closed).

LoadBalancer#select_caught_up_hosts has unnecessary logic managing the host list which we don't use (except selecting a single sample host from it). Thus, it could be replaced with LoadBalancer#select_up_to_date_host.

Because LoadBalancer#select_caught_up_hosts was implemented as a response to a particular issue with the merge requests - MR - I consider that it would be safer to deprecate this logic via the Feature Flag.

FF rollout issue: #335109 (closed)

Does this MR meet the acceptance criteria?

Conformity

• I have included changelog trailers, or none are 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.
• This change is backwards compatible across updates, or this does not apply.

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.

Security

N/A

Related to #335107 (closed)