[FEATURE] Code tab in Desktop app should support Enter to submit (same as Chat tab)

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

In the Claude Desktop app, the Code tab requires Ctrl+Enter to submit messages. Pressing Enter only inserts a newline. There is also no visible send button in the Code tab.

This is inconsistent with the Chat tab (where Enter submits) and with every major AI chat interface (ChatGPT, Gemini, etc.). The ~/.claude/keybindings.json config has no effect in the Desktop app, so there is no workaround.

Proposed Solution

1. Make Enter submit messages in the Code tab by default (matching Chat tab behavior)
2. Respect ~/.claude/keybindings.json in the Desktop app so users can customize this
3. Add a visible send button in the Code tab as a fallback

Alternative Solutions

Currently I have to use Ctrl+Enter every time, which breaks muscle memory and slows me down. No config workaround exists since keybindings.json is ignored in the Desktop app.

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. I'm working in the Claude Desktop app Code tab
2. I type a prompt and press Enter expecting it to send
3. Instead it just adds a newline
4. I have to remember to press Ctrl+Enter every time
5. This breaks flow constantly, especially when switching between Chat tab and Code tab

Additional Context

Related issues: #33034, #25087, #25145