fix(media_player): D1 — browse builds real BrowseMedia nodes, not BrowseMediaSource (t37)

`homeassistant.components.media_player` has not exported `BrowseMediaSource`
for years: the class lives in `homeassistant.components.media_source.models`,
where it exists to build `media_source://<domain>` ids and is the only place a
`domain` parameter belongs (t30 G18's note was about THAT class). The local
import therefore raised ImportError, and with it every real browse failed —
while the suite stayed green because the harness stubbed a `BrowseMediaSource`
that real HA does not expose from there.

`async_browse_media` now builds the standard tree exactly as core's own
androidtv_remote/media_player.py does: `BrowseMedia` imported from
homeassistant.components.media_player at module scope, every node carrying an
explicit media_content_id/media_content_type (MediaType.APP/APPS),
`children_media_class=MediaClass.APP` on the directory, and no `domain`.
Verified against a real install: the old import raises ImportError, the old
`domain=` kwarg raises TypeError, and the new node constructs.

The harness is now faithful so this cannot hide again:
* `entity_stublib` exposes a `BrowseMedia` with the real keyword-only
  signature, `as_dict()` and `calculate_children_class()`, plus `MediaType`,
  and deliberately NOT `BrowseMediaSource` — so both the drifted import and the
  drifted kwarg fail in-suite;
* the app-directory test asserts the standard shape (classes, explicit ids and
  types, children_media_class, the serialised payload) instead of the removed
  `domain` attribute;
* TestFaithfulHaStubs pins the harness contract on the AST (no production
  module imports BrowseMediaSource) rather than on prose.

Verified: 284 passed, 2 skipped (D1 stage); ruff clean. Full gate re-run on the
completed branch: 289 passed / 2 skipped and 290 passed / 1 skipped.

tests/test_command_routing.py

@@ -6,11 +6,13 @@ legacy external entity, plus the §7 channel digit sequence (protocol digits,
 layer marks which tier served each command.
 """
 
+import ast
 import asyncio
 import sys
 
 import entity_stublib
 import pytest
+from conftest import _SHIELD_DIR
 from entity_stublib import ENTITIES_STUB_NAMES, install, load_entity_modules
 from nsh.connection import ShieldConnectionManager
 from nsh.const import TIVIMATE_PACKAGE
@@ -1014,6 +1016,52 @@ class TestEntryDiagnostics:
         assert payload["transport"]["protocol"]["active"] is not None
 
 
+class TestFaithfulHaStubs:
+    """t37: the harness mirrors WHERE real HA exposes its API.
+
+    A regression of the exact drifts this task repairs must fail IN-SUITE, not
+    hide behind a stub that exposes anything anywhere.
+    """
+
+    def test_browse_media_source_is_not_importable_from_media_player(self):
+        import homeassistant.components.media_player as mp
+
+        assert isinstance(mp.BrowseMedia, type)  # the real node class
+        assert not hasattr(mp, "BrowseMediaSource")
+        with pytest.raises(ImportError):
+            # the drifted import must fail here exactly as in a real install
+            from homeassistant.components.media_player import BrowseMediaSource  # noqa: F401
+
+    def test_no_production_module_imports_browse_media_source(self):
+        """t37 D1: the drift is an IMPORT — checked on the AST, not on prose."""
+        offenders = []
+        for path in sorted(_SHIELD_DIR.glob("*.py")):
+            tree = ast.parse(path.read_text(encoding="utf-8"))
+            for node in ast.walk(tree):
+                if isinstance(node, ast.ImportFrom) and any(
+                    alias.name == "BrowseMediaSource" for alias in node.names
+                ):
+                    offenders.append(f"{path.name}:{node.lineno} imports it")
+                if isinstance(node, ast.Import) and any(
+                    alias.name.endswith("BrowseMediaSource") for alias in node.names
+                ):
+                    offenders.append(f"{path.name}:{node.lineno} imports it")
+        assert offenders == []
+
+    def test_the_browse_nodes_refuse_the_media_source_domain_kwarg(self):
+        import homeassistant.components.media_player as mp
+
+        with pytest.raises(TypeError):
+            mp.BrowseMedia(
+                title="x",
+                media_class=mp.MediaClass.APP,
+                media_content_type=mp.MediaType.APP,
+                media_content_id="pkg",
+                can_play=True,
+                can_expand=False,
+                domain="nvidia_shield",  # G18 keyword of BrowseMediaSource only
+            )
+
 class TestBrowseMediaDirectory:
     """P4-2c: the app directory root and its launch path."""
 
@@ -1034,10 +1082,24 @@ class TestBrowseMediaDirectory:
             ("com.netflix.ninja", "Netflix"),
         ]
         assert all(c.media_content_type == "app" for c in root.children)
-        # t30 G18 (2026-05-20 blog): the domain parameter is present at
-        # every level of the tree
-        assert root.domain == "nvidia_shield"
-        assert all(c.domain == "nvidia_shield" for c in root.children)
+        # t37 D1: a standard media_player.BrowseMedia tree — explicit
+        # media_content_id/-type at every level, the directory naming the class
+        # of its children, and NO media_source `domain` (that parameter belongs
+        # to media_source.models.BrowseMediaSource, which also builds the
+        # media_source:// ids).
+        assert root.media_class == "directory"
+        assert root.media_content_id == "apps"
+        assert root.media_content_type == "apps"
+        assert root.children_media_class == "app"
+        assert not hasattr(root, "domain")
+        assert [c.media_class for c in root.children] == ["app", "app"]
+        # ...and it serialises into the payload the frontend consumes
+        payload = root.as_dict()
+        assert payload["media_content_id"] == "apps"
+        assert payload["children_media_class"] == "app"
+        assert payload["children"][0]["media_content_id"] == "ar.tvplayer.tv"
+        assert payload["children"][0]["media_content_type"] == "app"
+        assert payload["children"][0]["can_play"] is True
 
     async def test_root_falls_back_to_the_curated_default(self, modules):
         player, _s, _i = make_player(modules)  # no apps map configured