Resolve "Speed up `yarn install` in CI by utilizing inter-pipeline cache"

What does this MR do?

Should speed up yarn install process within the setup-test-env CI job.

Are there points in the code the reviewer needs to double check?

The yarn install process should show a much lower execution time than it did previously (50s - 100s).

Why was this MR needed?

Anything to reduce pipeline time should help contributor productivity and reduce compute time expenses.

Screenshots (if relevant)

n/a

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Tests
  • All builds are passing
• Branch has no merge conflicts with master (if it does - rebase it please)
• Squashed related commits together

What are the relevant issue numbers?

Closes #32219 (closed)