Fix docs root showing Caddy default page, fix MCP healthcheck

- Clear /usr/share/caddy/* before copying build output to remove
  the default "Caddy works!" index.html from the base image
- Add root redirect: / -> /getting-started/ (permanent)
- Fix try_files to use {path}/index.html for Starlight directories
- Switch MCP healthcheck to TCP socket (GET /mcp returns 406
  without proper Accept headers)

Dockerfile.mcp

@@ -21,7 +21,7 @@ COPY src/ src/
 EXPOSE 8000
 
 HEALTHCHECK --interval=30s --timeout=5s --start-period=10s --retries=3 \
-    CMD python -c "import urllib.request; urllib.request.urlopen('http://127.0.0.1:8000/mcp')" || exit 1
+    CMD python -c "import socket; s=socket.create_connection(('127.0.0.1',8000),timeout=3); s.close()" || exit 1
 
 USER nobody
 CMD ["mcnoaa-tides"]

docs/Caddyfile.prod

@@ -1,9 +1,11 @@
 :4321 {
 	encode gzip
 
+	redir / /getting-started/ permanent
+
 	handle {
 		root * /usr/share/caddy
-		try_files {path} {path}/ /index.html
+		try_files {path} {path}/index.html
 		file_server
 	}
 }

docs/Dockerfile

@@ -21,6 +21,7 @@ RUN --mount=type=cache,target=/app/.astro \
 
 # --- Prod ---
 FROM caddy:2-alpine AS prod
+RUN rm -rf /usr/share/caddy/*
 COPY --from=build /app/dist /usr/share/caddy
 COPY Caddyfile.prod /etc/caddy/Caddyfile
 EXPOSE 4321