Cleanup Puma 5 upgrade transition code

What does this MR do?

This code was needed to perform Puma 5 upgrade without syncing multiple MRs. We updated to Puma 5, so this code is no longer required.

Related to #292918 (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

N/A

Security

N/A