refactor(web): extract clipboard hook and item subcomponents from context-picker

[selfcontained]

Summary

• Extracted use-context-picker-clipboard.ts (142 lines) — a custom hook encapsulating all clipboard-related state (4 useState, 3 useRef) and handlers (handleCheckClipboard, handleClipboardPasteInput, handleClipboardPasteBlur, handlePaste) from context-picker.tsx.
• Extracted context-picker-items.tsx (85 lines) — ContextFileItem and ContextLinkItem subcomponents for file thumbnail and link badge rendering.
• Deduplicated the popover content JSX that was repeated in both the empty-state and has-items branches into a shared popoverContent variable.

Result: context-picker.tsx reduced from 609 → 441 lines. The component now has 3 useState hooks (down from 7) and the render tree is easier to follow.

New file structure

context-picker.tsx              (441 lines — main component + small inline helpers)
use-context-picker-clipboard.ts (142 lines — clipboard logic hook)
context-picker-items.tsx         (85 lines — file/link item renderers)

Next run

changes-tab.tsx (893 lines) is queued as the next componentizer target.

Test plan

• TypeScript type check passes (pnpm run check:web)
• Production build succeeds (pnpm run build:web)
• E2E tests pass (122/123, 1 pre-existing split-pane flake)
• Purely structural — no behavior or UI changes

🤖 Generated with Claude Code