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/entity_stublib.py

@@ -64,35 +64,94 @@ class MediaPlayerEntityFeature(enum.IntFlag):
 
 
 class MediaClass:
+    """homeassistant.components.media_player.MediaClass (values we use)."""
+
     APP = "app"
     DIRECTORY = "directory"
 
 
-class BrowseMediaSource:
-    """HA BrowseMedia shape used by the app directory tests."""
+class MediaType:
+    """homeassistant.components.media_player.MediaType (values we use)."""
+
+    APP = "app"
+    APPS = "apps"
+
+
+class BrowseMedia:
+    """The REAL media_player.BrowseMedia shape (t37 D1).
+
+    Keyword-only with the six arguments real HA requires, the optional ones it
+    accepts, a faithful ``as_dict`` and — crucially — NO ``domain`` parameter:
+    ``BrowseMediaSource`` lives in
+    ``homeassistant.components.media_source.models`` (its contract is the
+    ``media_source://<domain>`` id) and is NOT importable from
+    ``homeassistant.components.media_player`` at all. The old import and the
+    old ``domain=`` kwarg therefore fail IN-SUITE instead of hiding behind a
+    permissive stub.
+    """
 
     def __init__(
         self,
         *,
-        title,
         media_class,
-        media_content_type,
         media_content_id,
+        media_content_type,
+        title,
         can_play,
         can_expand,
-        domain=None,  # t30 G18 (2026-05-20 blog contract)
         children=None,
+        children_media_class=None,
         thumbnail=None,
+        not_shown=0,
+        can_search=False,
+        search_media_classes=None,
     ):
-        self.title = title
         self.media_class = media_class
-        self.media_content_type = media_content_type
         self.media_content_id = media_content_id
+        self.media_content_type = media_content_type
+        self.title = title
         self.can_play = can_play
         self.can_expand = can_expand
-        self.domain = domain
-        self.children = children or []
+        self.children = children
+        self.children_media_class = children_media_class
         self.thumbnail = thumbnail
+        self.not_shown = not_shown
+        self.can_search = can_search
+        self.search_media_classes = search_media_classes
+
+    def as_dict(self, *, parent=True):
+        """Real payload conversion — what the frontend actually consumes."""
+        if self.children_media_class is None and self.children:
+            self.calculate_children_class()
+        response = {
+            "title": self.title,
+            "media_class": self.media_class,
+            "media_content_type": self.media_content_type,
+            "media_content_id": self.media_content_id,
+            "children_media_class": self.children_media_class,
+            "can_play": self.can_play,
+            "can_expand": self.can_expand,
+            "can_search": self.can_search,
+            "search_media_classes": self.search_media_classes,
+            "thumbnail": self.thumbnail,
+        }
+        if not parent:
+            return response
+        response["not_shown"] = self.not_shown
+        response["children"] = (
+            [child.as_dict(parent=False) for child in self.children]
+            if self.children
+            else []
+        )
+        return response
+
+    def calculate_children_class(self):
+        """Real helper: the children's common class, else DIRECTORY."""
+        self.children_media_class = MediaClass.DIRECTORY
+        assert self.children is not None
+        proposed_class = self.children[0].media_class
+        if all(child.media_class == proposed_class for child in self.children):
+            self.children_media_class = proposed_class
 
 
 class MediaEntityManager:
@@ -278,9 +337,12 @@ def install() -> None:
     mp.MediaPlayerEntity = MediaPlayerEntity
     mp.MediaPlayerDeviceClass = types.SimpleNamespace(TV="tv")
     mp.MediaPlayerEntityFeature = MediaPlayerEntityFeature
-    mp.BrowseMedia = BrowseMediaSource  # factory used as a constructor
-    mp.BrowseMediaSource = BrowseMediaSource
+    mp.BrowseMedia = BrowseMedia
     mp.MediaClass = MediaClass
+    mp.MediaType = MediaType
+    # NOTE (t37 D1): homeassistant.components.media_player exposes NO
+    # BrowseMediaSource — deliberately not stubbed, so the drifted import
+    # fails here exactly as it does in a real install.
     mp.MediaPlayerState = MediaPlayerState
     sys.modules["homeassistant.components.media_player"] = mp
 
@@ -347,6 +409,7 @@ def install() -> None:
     entity_platform = types.ModuleType("homeassistant.helpers.entity_platform")
     entity_platform.AddEntitiesCallback = object
     helpers.entity_platform = entity_platform
+
     sys.modules["homeassistant.helpers.event"] = event
     sys.modules["homeassistant.helpers.entity"] = entity
     sys.modules["homeassistant.helpers.entity_platform"] = entity_platform