fix(chat): prevent focus from landing inside hidden FAB panel

[Ludy87]

Description of Changes

• Changed the chat FAB so the panel content is mounted only while the window is open.
• Kept the floating window shell animated, but removed the hidden textarea from the DOM when closed.
• Added ref forwarding to ChatFABButton so focus can be returned to the trigger after closing the panel.
• Kept the close flow explicit so keyboard focus is moved out before the panel hides.

Why this change was made:

• The browser was warning that aria-hidden was being applied to a container while its textarea descendant still had focus.
• That broke accessibility expectations and created noisy console warnings during normal chat close/open interactions.
• Mounting the chat panel only when open removes the hidden-focused-descendant state entirely.

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Checklist

General

• I have read the Contribution Guidelines
• I have read the Stirling-PDF Developer Guide (if applicable)
• I have read the How to add new languages to Stirling-PDF (if applicable)
• I have performed a self-review of my own code
• My changes generate no new warnings

Documentation

• I have updated relevant docs on Stirling-PDF's doc repo (if functionality has heavily changed)
• I have read the section Add New Translation Tags (for new translation tags only)

Translations (if applicable)

• I ran scripts/counter_translation.py

UI Changes (if applicable)

• Screenshots or videos demonstrating the UI changes are attached (e.g., as comments or direct attachments in the PR)

Testing (if applicable)

• I have run task check to verify linters, typechecks, and tests pass
• I have tested my changes locally. Refer to the Testing Guide for more details.

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