[Obs AI Assistant] Avoid opening multiple flyouts

[viduni94]

Closes #204087

Problem

Sometimes, the flyout opens multiple times, creating a pitch black overlay. And the user have to click multiple times to close the opened flyouts.

Solution

Make sure only one instance of the flyout can be opened at all times.

Screen Recording

Before the fix:

before-the-fix-multiple-flyouts-opening.mov

After the fix:

after-the-fix-only-one-flyout-opens.mov

Note: This issue still persists with the keyboard shortcut. I tried various ways to make sure the listener is only attached once. But the flyout keeps opening multiple times even with those solutions. I'm assuming the keyboard shortcut it not heavily used by the users. Therefore, I created another issue to get back to it - #208973

Checklist

• The PR description includes the appropriate Release Notes section, and the correct release_note:* label is applied per the guidelines

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