Render a window shadow on the floating chat input window

[Copilot]

Description

The Omni chat input hosts its content in a frameless, transparent auxiliary window sized tightly to the input. With no chrome and no shadow, it doesn't read as a separate window and gets mistaken for an inline input box.

Since the window bounds hug the surface, a box-shadow alone would be clipped at the window edge. The fix reserves a transparent gutter around the surface and grows the window bounds by that gutter, so the shadow renders into the transparent band while the input keeps its exact content size.

• media/chatInputWindow.css — introduce --omni-window-shadow-size: 16px, drive the surface margin / height calc from it (replacing the 1px stroke), and add box-shadow: 0 3px 10px 0 var(--vscode-widget-shadow, …) (matching the shadow token used by suggest/action widgets).
• chatInputWindowService.ts — add CHAT_INPUT_WINDOW_SHADOW_SIZE = 16 (kept in sync with the CSS var); fitWindowToInput and _defaultBounds now pad width/height by 2 * shadow so the surface size is preserved and the shadow isn't clipped.

Pending-approval panel sizing and action-widget anchoring measure relative getBoundingClientRect()s, so the inset gutter is transparent to them.

• Fixes Window does not look like a window #331179

[Copilot]

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