docs: add Google-style docstrings and Sphinx autodoc setup

Add concise docstrings to all Python modules, classes, and public
functions. Configure Sphinx with napoleon extension for Google-style
docstring parsing and autodoc pages for each module.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

handlers/api.py

@@ -1,3 +1,5 @@
+"""REST API handlers for game operations."""
+
 import json
 from datetime import datetime, timezone
 
@@ -9,6 +11,8 @@ from models.game import Game, Word
 
 
 class BaseAPIHandler(tornado.web.RequestHandler):
+    """Base handler for JSON API endpoints."""
+
     def set_default_headers(self):
         self.set_header("Content-Type", "application/json")
 
@@ -21,6 +25,8 @@ class BaseAPIHandler(tornado.web.RequestHandler):
 
 
 class CategoriesHandler(BaseAPIHandler):
+    """``GET /api/categories`` -- list all word categories."""
+
     def get(self):
         session = self.get_session()
         try:
@@ -31,6 +37,11 @@ class CategoriesHandler(BaseAPIHandler):
 
 
 class NewGameHandler(BaseAPIHandler):
+    """``POST /api/game/new`` -- create a new game.
+
+    Expects JSON body with ``category_id`` and optional ``board_size`` (8-20).
+    """
+
     def post(self):
         session = self.get_session()
         try:
@@ -67,6 +78,8 @@ class NewGameHandler(BaseAPIHandler):
 
 
 class GameStateHandler(BaseAPIHandler):
+    """``GET /api/game/<id>`` -- retrieve current game state."""
+
     def get(self, game_id):
         session = self.get_session()
         try:
@@ -100,6 +113,12 @@ class GameStateHandler(BaseAPIHandler):
 
 
 class GuessHandler(BaseAPIHandler):
+    """``POST /api/game/<id>/guess`` -- submit a word guess.
+
+    Accepts either ``{"word": "..."}`` for text input or
+    ``{"cells": [{"row": N, "col": N}, ...]}`` for click selection.
+    """
+
     def post(self, game_id):
         session = self.get_session()
         try: