[api] Reuse overflow buffer storage instead of allocating per stalled write (#19093)

tests/components/api/__init__.py

@@ -0,0 +1,17 @@
+import esphome.codegen as cg
+from esphome.core import CORE
+from tests.testing_helpers import ComponentManifestOverride
+
+
+def override_manifest(manifest: ComponentManifestOverride) -> None:
+    # USE_API compiles every api source, so emit what they need. No socket
+    # override: an __init__.py there makes pytest import its conftest as socket.conftest.
+    async def to_code_testing(config):
+        cg.add_define("USE_API")
+        cg.add_define("USE_API_PLAINTEXT")
+        cg.add_define("API_MAX_SEND_QUEUE", 8)
+        cg.add_define("MAX_API_CONNECTIONS", 1)
+        cg.add_define("USE_SOCKET_IMPL_BSD_SOCKETS")
+        CORE.register_controller()  # api_server registers with the controller registry
+
+    manifest.to_code = to_code_testing