[logger] Replace std::function callbacks with LogListener interface (#12153)

esphome/components/api/api_server.h

@@ -15,6 +15,9 @@
 #ifdef USE_API_USER_DEFINED_ACTIONS
 #include "user_services.h"
 #endif
+#ifdef USE_LOGGER
+#include "esphome/components/logger/logger.h"
+#endif
 
 #include <map>
 #include <vector>
@@ -27,7 +30,13 @@ struct SavedNoisePsk {
 } PACKED;  // NOLINT
 #endif
 
-class APIServer : public Component, public Controller {
+class APIServer : public Component,
+                  public Controller
+#ifdef USE_LOGGER
+    ,
+                  public logger::LogListener
+#endif
+{
  public:
   APIServer();
   void setup() override;
@@ -37,6 +46,9 @@ class APIServer : public Component, public Controller {
   void dump_config() override;
   void on_shutdown() override;
   bool teardown() override;
+#ifdef USE_LOGGER
+  void on_log(uint8_t level, const char *tag, const char *message, size_t message_len) override;
+#endif
 #ifdef USE_API_PASSWORD
   bool check_password(const uint8_t *password_data, size_t password_len) const;
   void set_password(const std::string &password);