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/index.json.jbuilder

@@ -0,0 +1,18 @@
+# frozen_string_literal: true
+
+json.chats @chats do |chat|
+  json.id chat.id
+  json.title chat.title
+  json.last_message_at chat.messages.ordered.first&.created_at&.iso8601
+  json.message_count chat.messages.count
+  json.error chat.error.present? ? chat.error : nil
+  json.created_at chat.created_at.iso8601
+  json.updated_at chat.updated_at.iso8601
+end
+
+json.pagination do
+  json.page @pagy.page
+  json.per_page @pagy.vars[:items]
+  json.total_count @pagy.count
+  json.total_pages @pagy.pages
+end