feat: add projects showcase and Lux-powered static file server

- Add website/serve.lux: static file server using HttpServer effect
  - Demonstrates serving the Lux website with Lux itself
  - Handles index files, clean URLs, and 404 responses

- Add website/projects/index.html: example projects showcase
  - Features 6 real project cards (REST API, Todo App, JSON Parser, etc.)
  - Highlights Task Manager API demonstrating all 3 killer features
  - Links to full source code in the repository

- Update examples sidebar with Projects section

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

website/serve.lux

@@ -0,0 +1,66 @@
+// Static File Server for Lux Website
+//
+// Usage: lux website/serve.lux
+// Then open http://localhost:8080
+//
+// This demonstrates serving the Lux website using Lux's own HTTP server!
+
+fn main(): Unit with {HttpServer, Console, File} = {
+    let port = 8080
+    let root = "website"
+
+    HttpServer.listen(port)
+    Console.print("Lux website server running at http://localhost:" + toString(port))
+    Console.print("Serving files from: " + root)
+    Console.print("Press Ctrl+C to stop")
+    Console.print("")
+
+    serverLoop(root)
+}
+
+fn serverLoop(root: String): Unit with {HttpServer, Console, File} = {
+    let req = HttpServer.accept()
+
+    // Log request
+    Console.print(req.method + " " + req.path)
+
+    // Only handle GET requests
+    if req.method != "GET" then {
+        HttpServer.respond(405, "Method Not Allowed")
+        serverLoop(root)
+    } else {
+        serveFile(root, req.path)
+        serverLoop(root)
+    }
+}
+
+fn serveFile(root: String, reqPath: String): Unit with {HttpServer, Console, File} = {
+    // Determine file path
+    let path = if reqPath == "/" then "/index.html" else reqPath
+    let filePath = root + path
+
+    // Try to serve the file
+    if File.exists(filePath) then {
+        let content = File.read(filePath)
+        HttpServer.respond(200, content)
+    } else {
+        // Try with .html extension for clean URLs
+        let htmlPath = filePath + ".html"
+        if File.exists(htmlPath) then {
+            let content = File.read(htmlPath)
+            HttpServer.respond(200, content)
+        } else {
+            // Try index.html for directory paths
+            let indexPath = filePath + "/index.html"
+            if File.exists(indexPath) then {
+                let content = File.read(indexPath)
+                HttpServer.respond(200, content)
+            } else {
+                Console.print("  -> 404 Not Found: " + filePath)
+                HttpServer.respond(404, "Not Found: " + reqPath)
+            }
+        }
+    }
+}
+
+let output = run main() with {}