#633 fix(chats): exclude chats with zero messages from listing

Chats with no messages no longer appear in the chat listing. selectChatsWithSessions now inner-joins chat_messages, so a chat only surfaces once it has at least one message. This applies to both GET /api/chats and the get_chats MCP tool, which share the function. The embedded count keeps the query to one aggregate row per chat rather than fetching every message.

Test plan

• pnpm test lib/chats lib/supabase/chats lib/mcp/tools/chats — 201 green
• pnpm lint:check — clean
• Verify on Vercel preview: GET /api/chats omits freshly-created, message-less chats and still returns chats with messages.

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Summary by cubic

Exclude empty chats from listings by inner-joining chat_messages in selectChatsWithSessions, so a chat appears only after it has at least one message. Applies to GET /api/chats and the get_chats MCP tool; uses messages:chat_messages!inner ( id ) to enforce a true inner join, with tests updated to assert it and comments trimmed.

Summary by CodeRabbit

• Bug Fixes
  • Chat listings now exclude conversations without messages.
  • Message count information is now included in chat data.