examples: rewrite browser-auth.el using new language features

No native_js or native_js_call anywhere. Full browser auth flow expressed
with proper El constructs:

- extern fn supabase_create_client(url, key) -> Any
  Declares the Supabase CDN global without an El function body.

- client.auth.signInWithOtp(opts)
  Direct method call chain on Any-typed value. The client is built by
  calling the extern fn; .auth field access and .signInWithOtp(opts)
  method call emit clean JS without any escape hatch.

- try { ... } catch (err: Any) { ... }
  Wraps the auth call; unexpected runtime errors are caught and shown
  to the user rather than crashing silently.

- fn(event: Any) -> Void { ... }
  Inline anonymous function literals for DOM event listeners instead
  of named forward-declared callbacks.

The rewrite is the proof: every browser JavaScript pattern used in a
real auth flow can now be expressed structurally in El.

examples/browser-auth.el

@@ -1,11 +1,14 @@
-// browser-auth.el -- El-compiled auth flow using Supabase via native_js_call
+// browser-auth.el -- El-compiled auth flow using Supabase
 //
 // Compile: elc --target=js --bundle examples/browser-auth.el > auth.js
 // (requires el_runtime.js in the same directory as browser-auth.el)
 //
 // Demonstrates:
+//   - extern fn for declaring Supabase client constructor
+//   - anonymous function literals for callbacks
+//   - method call syntax on Any-typed values (client.auth.signInWithOtp)
+//   - try/catch for error handling
 //   - @async functions with DOM interaction
-//   - native_js_call to invoke third-party library methods (Supabase)
 //   - DOM bridge: dom_get_element, dom_get_value, dom_set_text, dom_add_class
 //     dom_remove_class, dom_show, dom_hide, dom_is_null
 //   - window_set to expose El functions to the browser global scope
@@ -19,8 +22,16 @@
 //   #auth-message       -- status message container
 //   #auth-form          -- the form to hide after success
 //
-// Supabase client is expected on window.supabase (loaded from Supabase CDN
+// The Supabase JS SDK is loaded from CDN via a <script> tag before auth.js.
-// via a separate script tag before auth.js).
+// supabase_create_client is declared extern: the runtime provides it via
+// the global supabase.createClient function exposed by the CDN bundle.
+
+// ── External declarations ─────────────────────────────────────────────────
+//
+// These functions are provided by the JS environment (CDN script tags).
+// No body is emitted -- the compiler just records the names.
+
+extern fn supabase_create_client(url: String, key: String) -> Any
 
 // ── UI helpers ─────────────────────────────────────────────────────────────
 
@@ -72,6 +83,22 @@ fn is_valid_email(email: String) -> Bool {
     return true
 }
 
+// ── Supabase client construction ──────────────────────────────────────────
+//
+// Build a Supabase client from config injected into the page as NEURON_CFG.
+// The extern fn supabase_create_client maps to supabase.createClient on
+// the global object exposed by the CDN bundle.
+
+fn get_supabase_client() -> Any {
+    let cfg = window_get("NEURON_CFG")
+    if dom_is_null(cfg) {
+        return null
+    }
+    let url: String = cfg["supabaseUrl"]
+    let key: String = cfg["supabaseAnonKey"]
+    supabase_create_client(url, key)
+}
+
 // ── Auth flow ──────────────────────────────────────────────────────────────
 
 @async
@@ -93,32 +120,26 @@ fn send_magic_link() -> Void {
     set_button_loading(true)
     state_set("auth_email", email)
 
-    // Call Supabase via native_js_call.
+    // Build the Supabase client and call auth.signInWithOtp directly.
-    // window.supabase.auth.signInWithOtp({ email: "..." }) returns a Promise.
+    // Method call syntax on Any-typed values: client.auth.signInWithOtp(opts)
-    let supabase = window_get("supabase")
+    // No native_js_call required.
-    if dom_is_null(supabase) {
+    let client = get_supabase_client()
-        show_message("Auth service not available", true)
+    if dom_is_null(client) {
+        show_message("Auth service not configured", true)
         set_button_loading(false)
         return null
     }
 
-    let auth = native_js_call(supabase, "auth", [])
+    try {
-    let payload = { "email": email }
+        let opts: Map<String, Any> = { "email": email }
-    let result = native_js_call(auth, "signInWithOtp", [payload])
+        // client is Any-typed; .auth returns the auth sub-client (also Any).
-
+        // .signInWithOtp(opts) returns a Promise. @async + await handles it.
-    // Await the promise via native_js_call on the result object
+        let resp = client.auth.signInWithOtp(opts)
-    let error = native_js_call(result, "then", [check_auth_result])
-    set_button_loading(false)
-}
-
-fn check_auth_result(resp: Any) -> Void {
         let err = resp["error"]
         if !dom_is_null(err) {
             let msg: String = err["message"]
             show_message("Error: " + msg, true)
-        return null
+        } else {
-    }
-    let email: String = state_get("auth_email")
             local_storage_set("auth_pending_email", email)
             show_message("Magic link sent! Check your inbox for " + email, false)
             let form = dom_get_element("auth-form")
@@ -126,6 +147,12 @@ fn check_auth_result(resp: Any) -> Void {
                 dom_hide(form)
             }
         }
+    } catch (err: Any) {
+        show_message("Unexpected error. Please try again.", true)
+    }
+
+    set_button_loading(false)
+}
 
 // ── Keyboard support ───────────────────────────────────────────────────────
 
@@ -141,25 +168,33 @@ fn handle_email_keydown(event: Any) -> Void {
 fn init_auth() -> Void {
     let email_el = dom_get_element("acct-email-input")
     if !dom_is_null(email_el) {
-        // Pre-fill from local storage if a pending send was interrupted
+        // Pre-fill from local storage if a pending send was interrupted.
         let pending: String = local_storage_get("auth_pending_email")
         if !str_eq(pending, "") {
             dom_set_value(email_el, pending)
         }
-        dom_listen(email_el, "keydown", handle_email_keydown)
+        // Anonymous function literal for inline event handler.
+        dom_listen(email_el, "keydown", fn(event: Any) -> Void {
+            let key: String = dom_get_prop(event, "key")
+            if str_eq(key, "Enter") {
+                send_magic_link()
+            }
+        })
     }
     let btn = dom_get_element("send-link-btn")
     if !dom_is_null(btn) {
-        dom_listen(btn, "click", send_magic_link)
+        dom_listen(btn, "click", fn(event: Any) -> Void {
+            send_magic_link()
+        })
     }
     state_set("auth_initialized", "true")
 }
 
 fn main() -> Void {
-    // Expose send_magic_link globally so inline event handlers can call it
+    // Expose send_magic_link globally so inline event handlers can call it.
     window_set("sendMagicLink", send_magic_link)
     window_set("initAuth", init_auth)
 
-    // Run init when DOM is ready
+    // Run init when DOM is ready.
     window_on_load(init_auth)
 }