Claude provider: /clear and /new slash commands don't clear h-code context

[harrryyd]

Problem

When using the Claude Code provider, typing /clear or /new in the composer sends the command through to Claude CLI (which natively handles them), but h-code does not observe the context-clearing event and does not clear its own conversation history.

Steps to reproduce

1. Start a thread with Claude Code provider
2. Have a multi-turn conversation
3. Type /clear and send it
4. Observe the UI still shows all prior messages
5. Follow up with a new message — Claude CLI has no prior context, but h-code still renders the full history

Root cause

• /clear and /new are sent to Claude CLI as regular user messages. Claude CLI clears its internal context and returns a result.
• The Claude adapter (ClaudeAdapter.ts) treats the turn like any other — it calls completeTurn() and moves on. It does not inspect result messages for context-cleared semantics.
• h-code independently stores and displays turn history. It never learns that the provider cleared its context.

Expected behavior

Options (needs discussion):

1. Client-side interception: Treat /clear and /new like /plan / /default — intercept before sending, and create a new thread (or clear turns from the current thread).
2. Server-side sync: Have the Claude adapter detect when Claude CLI clears context (via result message subtype or system message) and emit a domain event that clears stored turns.
3. Both: Intercept client-side for immediate UI feedback + server-side sync as a safety net.

Area

• apps/server/src/provider/Layers/ClaudeAdapter.ts — sendTurn, handleResultMessage, handleSystemMessage
• apps/web/src/composer-logic.ts — parseStandaloneComposerSlashCommand
• apps/web/src/components/ChatView.tsx — onSend message dispatch

[harrryyd]

Implemented and merged to main.