Emoji Picker: Fix wrongly shown active tab after closing

What does this MR do and why?

Emoji Picker: Fix wrongly shown active tab after closing

When you open the Emoji picker and select a different tab, close it and reopen it again, the last select tab stays active which prevents the ability to click on the first tab and indicates the wrong tab as active.

This MR also fixes an issue where the search term does not get reset after closing the picker without an selection.

Screenshots or screen recordings

Before	After

How to set up and validate locally

Scenario 1

1. Go to an issuable/MR (e.g. http://gdk.test:3000/flightjs/Flight/-/issues/1)
2. Open the Emoji picker
3. Select a different tab
4. Close the Emoji picker
5. Open it again, the wrong tab is selected, the first tab can't be clicked

Scenario 2

1. Go to an issuable/MR (e.g. http://gdk.test:3000/flightjs/Flight/-/issues/1)
2. Open the Emoji picker
3. Perform a search
4. Close the Emoji picker
5. The search term remains and does not get cleared

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 #430244 (closed)