[core] Fix DelayAction compile error with non-const reference args (#15814)

esphome/core/base_automation.h

@@ -205,7 +205,9 @@ template<typename... Ts> class DelayAction : public Action<Ts...>, public Compon
     } else {
       // For delays with arguments, capture by value to preserve argument values
       // Arguments must be copied because original references may be invalid after delay
-      auto f = [this, x...]() { this->play_next_(x...); };
+      // `mutable` is required so captured copies of non-const reference args (e.g. std::string&)
+      // are passed as non-const lvalues to play_next_(const Ts&...) where Ts may be `T&`
+      auto f = [this, x...]() mutable { this->play_next_(x...); };
       App.scheduler.set_timer_common_(this, Scheduler::SchedulerItem::TIMEOUT, Scheduler::NameType::NUMERIC_ID_INTERNAL,
                                       nullptr, static_cast<uint32_t>(InternalSchedulerID::DELAY_ACTION),
                                       this->delay_.value(x...), std::move(f),

tests/components/http_request/http_request.yaml

@@ -45,6 +45,11 @@ esphome:
                   args:
                     - response->status_code
                     - body.c_str()
+              - delay: 1s
+              - logger.log:
+                  format: "After delay, body still: %s"
+                  args:
+                    - body.c_str()
 
 http_request:
   useragent: esphome/tagreader