[Website] Keep the Dock corner launcher clickable after dragging

[adamziel]

This keeps the Dock corner launcher clickable immediately after a drag and adds coverage for the missing desktop-corner and mobile-close flows.

#4009 suppresses the click synthesized after dragging so a drag cannot activate a Dock control. That listener was global. With reduced motion enabled, the corner launcher appears immediately, and its first click was swallowed even though the launcher is outside the Dock. This limits suppression to click targets inside the dragged Dock.

The Playwright tests now fold and reopen the desktop Dock, confirm an open pane prevents folding, close a mobile pane, and verify that closing returns focus to its Dock button and makes the preview interactive again. The flows pass in Chromium, Firefox, and WebKit.

This PR is stacked on #4009 so the production change and added coverage do not enlarge that PR.

Testing

• Selected corner and mobile Playwright tests: 6/6 across Chromium, Firefox, and WebKit
• npx nx run-many -t lint,typecheck,test -p playground-website: 57 test files, 303 tests

[Copilot]

Pull request overview

Note

Copilot was unable to run its full agentic suite in this review.

Limits post-drag click suppression to clicks inside the Dock (so the corner launcher remains clickable immediately after dragging) and expands Playwright coverage for desktop-corner and mobile-close behaviors.

Changes:

• Scope the “eatClick” suppression logic to Dock-contained click targets only.
• Add a reduced-motion desktop test covering fold/restore and “pane open prevents folding”.
• Extend mobile Dock test to verify closing a pane restores focus and re-enables the preview.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

File	Description
packages/playground/website/src/components/dock/dock.tsx	Restricts synthesized-click suppression to targets inside the Dock element.
packages/playground/website/playwright/e2e/website-ui.spec.ts	Adds/extends e2e coverage for desktop fold/restore and mobile pane close + focus/inert behavior.

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