PLEASE NOTE THAT THIS DIFF AND SUBSEQUENT DIFFS IN THIS STACK WILL NOT BE LANDED UNTIL MORE OF THE REDESIGN IS READY SINCE THIS WILL CAUSE REGRESSIONS IN PROD
When the user has inputted something into the search bar of the add user list, the UI should update to show that the user is in the "search mode"
For context here is what the figma design looks like:
Linear task: https://linear.app/comm/issue/ENG-5959/search-users-ui-changes
Depends on D10746