[vip-split] [Split Expense] Refactor Participant Selector

[mountiny]

Part of the Add Split expense to global create project, design doc.

Please, implement following sections of the design doc:

• Refactor Participant Selector

This project is handled by our experienced C+: @shubham1206agra and @getusha. Please, refrain from posting proposals

[melvin-bot]

Triggered auto assignment to @zanyrenney (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 ⚠️