Add landing page, tests, Docker deployment, nginx config

src/index.ts

@@ -1,5 +1,7 @@
 import express from "express";
 import helmet from "helmet";
+import path from "path";
+import { fileURLToPath } from "url";
 import rateLimit from "express-rate-limit";
 import { convertRouter } from "./routes/convert.js";
 import { templatesRouter } from "./routes/templates.js";
@@ -30,8 +32,12 @@ app.use("/health", healthRouter);
 app.use("/v1/convert", authMiddleware, convertRouter);
 app.use("/v1/templates", authMiddleware, templatesRouter);
 
-// Root
-app.get("/", (_req, res) => {
+// Landing page
+const __dirname = path.dirname(fileURLToPath(import.meta.url));
+app.use(express.static(path.join(__dirname, "../public")));
+
+// API root (for programmatic discovery)
+app.get("/api", (_req, res) => {
   res.json({
     name: "DocFast API",
     version: "0.1.0",