Remote Control: support file sending (not just photos) and real-time streaming from mobile

Feature Request

1. File Sending via Mobile Remote Control

When using Claude Code remote control from the Claude mobile app (iOS/Android), we can currently only send photos. This is limiting — we often need to send:

• PDFs (design specs, documentation, requirements)
• Screenshots from other apps (Figma exports, terminal screenshots)
• Code files (snippets, config files, logs)
• Documents (Word, Excel, CSV — data to work with)
• Any file type the desktop Claude Code session could use

Current behavior: Only camera/photo picker is available in remote control mode.
Expected behavior: Full file picker (Files app on iOS, file manager on Android) allowing any file type to be sent to the remote Claude Code session.

2. Real-Time Streaming in Remote Control

When controlling a Claude Code session remotely from the phone, the output appears after Claude finishes thinking/generating — not in real-time as it streams on the terminal.

This makes it hard to:

• Know if Claude is still working or stuck
• Interrupt early if it's going in the wrong direction
• Feel connected to what's happening in the session

Current behavior: Output appears in chunks or after completion.
Expected behavior: Real-time token-by-token streaming, matching what you see in the terminal. Even partial streaming (every few seconds) would be a massive improvement.

Why This Matters

Remote control from phone is one of Claude Code's most powerful features — Boris Cherny runs sessions from his phone regularly. But these two limitations make it feel like a read-only monitor rather than a true remote control. With file sending and streaming, mobile becomes a genuine second workstation.

Environment

• Claude Code v2.1.89
• iOS Claude app
• macOS host running Claude Code with remote control enabled