Fix variables returning non-string types, use identity check for std_string

- Revert variables templatable output_type back to None since variable
  lambdas can return any type (float, int, etc.), not just strings.
- Use lazy import identity check (output_type is std_string) instead of
  brittle string comparison in templatable().
- Clarify ESP8266 populate_service_map comment explaining why STATIC_STRING
  fast path is not needed (all codegen strings are FLASH_STRING on ESP8266).

esphome/components/api/homeassistant_service.h

@@ -232,10 +232,11 @@ template<typename... Ts> class HomeAssistantServiceCallAction : public Action<Ts
     dest.init(source.size());
 
 #ifdef USE_ESP8266
-    // On ESP8266, keys may be in PROGMEM (from ESPHOME_F in codegen) and
-    // FLASH_STRING values need copying via _P functions.
-    // Allocate storage for all keys + all values (2 entries per source item).
-    // strlen_P/memcpy_P handle both RAM and PROGMEM pointers safely.
+    // On ESP8266, all static strings from codegen are FLASH_STRING (PROGMEM),
+    // so is_static_string() is always false — the zero-copy STATIC_STRING fast
+    // path from the non-ESP8266 branch cannot trigger. We copy all keys and
+    // values unconditionally: keys via _P functions (may be in PROGMEM), values
+    // via value() which handles FLASH_STRING internally.
     value_storage.init(source.size() * 2);
 
     for (auto &it : source) {

esphome/cpp_generator.py

@@ -780,8 +780,13 @@ async def templatable(
     if to_exp is None:
         # Automatically wrap static strings in ESPHOME_F() for PROGMEM storage on ESP8266.
         # On other platforms ESPHOME_F() is a no-op returning const char*.
-        if isinstance(value, str) and str(output_type) == "std::string":
-            return FlashStringLiteral(value)
+        # Lazy import to avoid circular dependency (cpp_generator <-> cpp_types).
+        # Identity check (is) avoids brittle string comparison.
+        if isinstance(value, str) and output_type is not None:
+            from esphome.cpp_types import std_string
+
+            if output_type is std_string:
+                return FlashStringLiteral(value)
         return value
     if isinstance(to_exp, dict):
         return to_exp[value]