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>

docs/source/modules/app.rst

@@ -0,0 +1,7 @@
+App
+===
+
+.. automodule:: app
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/modules/db.rst

@@ -0,0 +1,7 @@
+Database
+========
+
+.. automodule:: db
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/modules/game.rst

@@ -0,0 +1,10 @@
+Game Logic
+==========
+
+Board Factory
+-------------
+
+.. automodule:: game.factory
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/modules/handlers.rst

@@ -0,0 +1,26 @@
+Handlers
+========
+
+API Handlers
+------------
+
+.. automodule:: handlers.api
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Main Handler
+------------
+
+.. automodule:: handlers.main
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Game Handler
+------------
+
+.. automodule:: handlers.game
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/modules/models.rst

@@ -0,0 +1,18 @@
+Models
+======
+
+Category
+--------
+
+.. automodule:: models.category
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Game
+----
+
+.. automodule:: models.game
+   :members:
+   :undoc-members:
+   :show-inheritance: