[Vacation Delegate] Add back reverted code and put behind the new beta for Vacation Delegate

[deetergp]

Add back the code we reverted in this CP and wrap it in a check for the new beta added in these back end PRs: https://github.com/Expensify/Web-Expensify/pull/47475 & https://github.com/Expensify/Web-Expensify/pull/47536

Issue Owner

Current Issue Owner: @deetergp

[melvin-bot]

Triggered auto assignment to @CortneyOfstad (NewFeature), see https://stackoverflowteams.com/c/expensify/questions/14418#:~:text=BugZero%20process%20steps%20for%20feature%20requests for more details. Please add this Feature request to a GH project, as outlined in the SO.

[melvin-bot]

⚠️ It looks like this issue is labelled as a New Feature but not tied to any GitHub Project. Keep in mind that all new features should be tied to GitHub Projects in order to properly track external CAP software time ⚠️

[melvin-bot]

Triggered auto assignment to Design team member for new feature review - @dubielzyk-expensify (NewFeature)