Refactor labels_select_root for embedded and standalone dropdowns

What does this MR do?

In !67966 (merged), we removed the part of labels widget that is responsible for handling embedded and standalone dropdowns. In this MR, we add this part back with proper "click outside" handling.

To test the changes locally, you will need a feature flag enabled:

Feature.enable(:labels_widget)

Screenshots or Screencasts (strongly suggested)

No visual changes

How to setup and validate locally (strongly suggested)

1. Enable the Labels widget FF

   Feature.enable(:labels_widget)

2. Open Group -> Epics list
3. Click on `New Epic button
4. Open labels dropdown and click on few labels.
5. Try to switch to "Create label" view and back
6. Make sure labels are applied when epic is created

Does this MR meet the acceptance criteria?

Conformity

• I have included changelog trailers, or none are needed. (Does this MR need a changelog?)
• I have added/updated documentation, or it's not needed. (Is documentation required?)
• I have properly separated EE content from FOSS, or this MR is FOSS only. (Where should EE code go?)
• I have added information for database reviewers in the MR description, or it's not needed. (Does this MR have database related changes?)
• I have self-reviewed this MR per code review guidelines.
• This MR does not harm performance, or I have asked a reviewer to help assess the performance impact. (Merge request performance guidelines)
• I have followed the style guides.
• This change is backwards compatible across updates, or this does not apply.

Availability and Testing

• I have added/updated tests following the Testing Guide, or it's not needed. (Consider all test levels. See the Test Planning Process.)
• I have tested this MR in all supported browsers, or it's not needed.
• I have informed the Infrastructure department of a default or new setting change per definition of done, or it's not needed.

Related to #339226 (closed)