Add API v1 chat endpoints

- Add chats#index and chats#show endpoints to list and view AI conversations
- Add messages#create endpoint to send messages to AI chats
- Include API documentation for chat endpoints
- Add controller tests for new endpoints

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

app/views/api/v1/chats/_chat.json.jbuilder

@@ -0,0 +1,7 @@
+# frozen_string_literal: true
+
+json.id chat.id
+json.title chat.title
+json.error chat.error.present? ? chat.error : nil
+json.created_at chat.created_at.iso8601
+json.updated_at chat.updated_at.iso8601