[FEATURE] Enable spell checking in VSCode extension input box

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

When using the Claude Code VSCode extension, there's no spell checking available in the input textarea where prompts are written.

Problem:

• Typos in prompts can lead to miscommunication
• Users expect spell checking in text input areas
• The VSCode editor has spell checking via extensions, but webview inputs don't benefit from this

Proposed Solution

Add spellcheck="true" attribute to the textarea/input element in the extension's webview. Since VSCode runs on Electron 8+, the built-in Chromium spellchecker should work automatically once enabled.

Expected Behavior:

• Misspelled words show red/squiggly underlines
• Right-click provides spelling suggestions
• Respects system language settings

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

_No response_

Additional Context

Environment:

• VSCode on Windows
• Claude Code extension