Labels widget - Fix search input

What does this MR do and why?

This change applies to labels widget behind :labels_widget feature flag.

• Fixes search input position when scrolling
• Split dropdown header to be reused (prep work for !71983 (merged))
• Split dropdown footer to be reused (same as above)

Screenshots or screen recordings

Before	After

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Related to #342970 (closed)