[captive_portal] Fix captive portal inaccessible when web_server auth is configured

Closes https://github.com/esphome/esphome/issues/12710

esphome/components/captive_portal/captive_portal.cpp

@@ -61,7 +61,7 @@ void CaptivePortal::handle_wifisave(AsyncWebServerRequest *request) {
   // Defer save to main loop thread to avoid NVS operations from HTTP thread
   this->defer([ssid, psk]() { wifi::global_wifi_component->save_wifi_sta(ssid.c_str(), psk.c_str()); });
 #endif
-  request->redirect(ESPHOME_F("/?save"));
+  request->send(200, ESPHOME_F("text/plain"), ESPHOME_F("Saved. Connecting..."));
 }
 
 void CaptivePortal::setup() {
@@ -71,7 +71,7 @@ void CaptivePortal::setup() {
 void CaptivePortal::start() {
   this->base_->init();
   if (!this->initialized_) {
-    this->base_->add_handler(this);
+    this->base_->add_handler_without_auth(this);
   }
 
   network::IPAddress ip = wifi::global_wifi_component->wifi_soft_ap_ip();

esphome/components/web_server_base/web_server_base.cpp

@@ -11,6 +11,10 @@ void WebServerBase::add_handler(AsyncWebHandler *handler) {
     handler = new internal::AuthMiddlewareHandler(handler, &credentials_);
   }
 #endif
+  this->add_handler_without_auth(handler);
+}
+
+void WebServerBase::add_handler_without_auth(AsyncWebHandler *handler) {
   this->handlers_.push_back(handler);
   if (this->server_ != nullptr) {
     this->server_->addHandler(handler);

esphome/components/web_server_base/web_server_base.h

@@ -122,6 +122,7 @@ class WebServerBase {
 #endif
 
   void add_handler(AsyncWebHandler *handler);
+  void add_handler_without_auth(AsyncWebHandler *handler);
 
   void set_port(uint16_t port) { port_ = port; }
   uint16_t get_port() const { return port_; }