[esp8266] Add crash handler for post-mortem diagnostics (#15465)

esphome/components/api/api_connection.h

@@ -20,6 +20,9 @@
 #ifdef USE_RP2040_CRASH_HANDLER
 #include "esphome/components/rp2040/crash_handler.h"
 #endif
+#ifdef USE_ESP8266_CRASH_HANDLER
+#include "esphome/components/esp8266/crash_handler.h"
+#endif
 #include "esphome/core/entity_base.h"
 #include "esphome/core/string_ref.h"
 
@@ -276,6 +279,9 @@ class APIConnection final : public APIServerConnectionBase {
 #endif
 #ifdef USE_RP2040_CRASH_HANDLER
     rp2040::crash_handler_log();
+#endif
+#ifdef USE_ESP8266_CRASH_HANDLER
+    esp8266::crash_handler_log();
 #endif
   }
 #ifdef USE_API_HOMEASSISTANT_SERVICES