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>

app.py

@@ -1,3 +1,5 @@
+"""Tornado application entry point and route configuration."""
+
 import os
 
 import click
@@ -20,6 +22,15 @@ BASE_DIR = os.path.dirname(os.path.abspath(__file__))
 
 
 def make_app(session_factory=None):
+    """Create and configure the Tornado application.
+
+    Args:
+        session_factory: SQLAlchemy session factory. If None, API
+            endpoints that require a database will not work.
+
+    Returns:
+        A configured ``tornado.web.Application`` instance.
+    """
     return tornado.web.Application(
         [
             (r"/", MainHandler),
@@ -41,6 +52,7 @@ def make_app(session_factory=None):
 @click.command()
 @click.option("--port", default=8888, type=int, help="Port to listen on.")
 def main(port):
+    """Start the web server."""
     engine = get_engine()
     init_db(engine)
     session_factory = get_session_factory(engine)