Draft: Relocate and retag test for mixed deployment refactor

What does this MR do and why?

Moves mixed environment tests into their own folder to prevent tests leaking into other jobs. Response to pipeline deployment changes requiring we alter our existing approach.

Was initially going to quarantine until the refactor was complete, thus the branch name. However, completed the refactor so renamed and repurposed this MR.

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Closes #344213 (closed)