[FEATURE] File upload support in the desktop app browser pane, without blocking parallel work

Product: Claude desktop app, Code tab, built-in browser pane (mcp__Claude_Browser__* tools).
Machine: MacBook Air M1, macOS 27.0.

1. Add a file_upload tool to the browser pane. It should take a file input ref and local paths,

the same as Claude in Chrome. The user approves the path once per session.

1. Never block on a native file dialog. If a page opens one, catch it in the pane. Let the agent

answer it with a path, or let me answer it, while other tabs keep working.

1. Handle uploads in parallel. One tab can wait on an upload while the agent works in another tab.
2. Optional: let me share a login session between the pane and my Chrome profile, so one login is

enough for both.

Why it matters: I deploy WordPress theme zips to staging many times per day. Each deploy is an
upload plus a confirm click. Today the pane cannot do the upload at all, so every deploy needs a
second browser.

Related bug: https://github.com/anthropics/claude-code/issues/101976