[core] Support set_internal() during setup, log error after setup (#19069)

tests/integration/fixtures/set_internal_at_boot.yaml

@@ -0,0 +1,34 @@
+esphome:
+  name: set-internal-at-boot
+  on_boot:
+    then:
+      - lambda: |-
+          id(hidden_at_boot).set_internal(true);
+          id(shown_at_boot).set_internal(false);
+
+host:
+
+api:
+  actions:
+    - action: set_internal_late
+      then:
+        - lambda: id(untouched).set_internal(true);
+
+logger:
+
+sensor:
+  - platform: template
+    name: "Hidden At Boot"
+    id: hidden_at_boot
+    lambda: return 1.0;
+
+  - platform: template
+    name: "Shown At Boot"
+    id: shown_at_boot
+    internal: true
+    lambda: return 2.0;
+
+  - platform: template
+    name: "Untouched"
+    id: untouched
+    lambda: return 3.0;

tests/integration/test_set_internal_at_boot.py

@@ -0,0 +1,41 @@
+"""Integration test for set_internal() called during and after setup."""
+
+from __future__ import annotations
+
+import pytest
+
+from .log_utils import LineWaiter
+from .types import APIClientConnectedFactory, RunCompiledFunction
+
+
+@pytest.mark.asyncio
+async def test_set_internal_at_boot(
+    yaml_config: str,
+    run_compiled: RunCompiledFunction,
+    api_client_connected: APIClientConnectedFactory,
+) -> None:
+    """set_internal() in on_boot changes API exposure, later calls log an error."""
+    waiter = LineWaiter()
+
+    async with (
+        run_compiled(yaml_config, line_callback=waiter.callback),
+        api_client_connected() as client,
+    ):
+        entities, services = await client.list_entities_services()
+        names = {entity.name for entity in entities}
+
+        assert "Hidden At Boot" not in names
+        assert "Shown At Boot" in names
+        assert "Untouched" in names
+
+        late = next(s for s in services if s.name == "set_internal_late")
+        await client.execute_service(late, {})
+        await waiter.wait_for(
+            "'Untouched'",
+            "set_internal() after setup is undefined behavior",
+            timeout=5.0,
+        )
+
+        # Still written during the deprecation window, ignored from 2027.3.0
+        entities, _ = await client.list_entities_services()
+        assert "Untouched" not in {entity.name for entity in entities}