Refactor organization groups/projects search to shared component

What does this MR do and why?

Related to #434469 (closed)

The grouptenant scale team is currently working on two initiatives. Building out Organizations MVC and using Vue components built for organizations to refactor group and project lists written in HAML.

This MR moves the filtered search bar used on Organization -> Groups and projects to a shared Vue component. In a future MR it will be used for Modernize sorting and filtering in Explore > Gr... (#434469 - closed) and other issues in &9012

MR acceptance checklist

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Screenshots or screen recordings

No visual changes, see video to demonstrate everything still works

Screen_Recording_2024-03-21_at_8.49.38_AM

How to set up and validate locally

1. Enable the feature flag
   • echo "Feature.enable(:ui_for_organizations)" | gdk rails c
2. Navigate to /-/organizations/default/groups_and_projects
3. Use the search and sort