feat: add chrome_move_tab tool for state-preserving tab moves

[pooyak]

Summary

Adds a new MCP tool chrome_move_tab that moves an existing tab between windows (or detaches it into a brand-new window) without reloading the page. Tab state — scroll position, navigation history, form input, and any in-page renderer state — is preserved, because the underlying chrome.tabs.move / chrome.windows.create({ tabId }) APIs reattach the existing renderer rather than recreating it.

Motivation

There's currently no MCP tool exposed for moving tabs. Achieving the equivalent today requires reading the URL, opening a new tab in the destination window, then closing the original — which causes a full page reload, a network round-trip, and loss of all in-page state. For users orchestrating tab layouts across many windows (the original motivating use case), this is both lossy and slow.

The Chrome extension API already provides chrome.tabs.move for this exact purpose; this PR just exposes it.

API

{
  tabId: number;          // required
  windowId?: number;      // destination window — required unless newWindow=true
  newWindow?: boolean;    // detach into a new window — mutually exclusive with windowId
  index?: number;         // position in destination window; -1 (default) = append
  focused?: boolean;      // focus destination window after move; default true
}

Validation:

• tabId is required.
• Exactly one of windowId / newWindow=true must be provided.
• index is ignored when newWindow=true.

Changes

• packages/shared/src/tools.ts — register TOOL_NAMES.BROWSER.MOVE_TAB and add a TOOL_SCHEMAS entry.
• app/chrome-extension/entrypoints/background/tools/browser/move-tab.ts — new MoveTabTool extending BaseBrowserToolExecutor.
• app/chrome-extension/entrypoints/background/tools/browser/index.ts — re-export so the dispatcher picks it up.

The tool follows the same shape as SwitchTabTool and reuses existing error-handling conventions.

Test plan

• pnpm build:shared — passes
• pnpm build:extension (wxt build) — passes; chrome_move_tab appears in the bundled background.js
• npx eslint <changed files> — clean (the 4 unrelated lint errors on master are not in changed paths)
• npx prettier --check <changed files> — clean
• Manual verification: load the unpacked extension, call chrome_move_tab with { tabId, newWindow: true } and { tabId, windowId } from an MCP client, confirm tab moves without reload (scroll/form state preserved).

Notes

• No changes to the native bridge or installation flow.
• Backwards-compatible: purely additive.

🤖 Generated with Claude Code