fix(media_player): normalize the app directory in one place (t51)

t49's two residuals share one cause: `_app_directory` handed the raw options map to
its consumers, so the Browse tree showed a child with a blank title and the reverse
lookup compared the user's padded name against itself. The map is hand-editable, so
the normalization belongs in that one accessor — the browse tree, source_list and the
reverse lookup then cannot disagree.

Policy, now documented in `_app_directory` (the single place):
* names are stripped as the directory is built, so display and match key are one
  string: `com.x=  TiviMate  ` shows as "TiviMate" AND resolves as "TiviMate";
* an entry whose NAME or whose PACKAGE is blank/whitespace-only is dropped, so no
  surface offers a child with no title or no package behind it (the t48 invariant,
  now extended to the Browse tree);
* two packages normalizing to the same name are BOTH KEPT — the tree reaches each by
  its own package id, so neither app is hidden — while the FIRST in map order wins the
  name: that is the single entry source_list offers and the package select_source
  resolves. Map order is the user's order, so the winner does not move between
  rebuilds; reversing the map reverses the winner, which is pinned.
* a well-formed map (what the editor and the curated default produce) is byte-identical
  in and out: stripping touches the EDGES only, so "TiviMate Pro" keeps its inner space.

source_list now just dedupes the normalized values (its own t49 filter moved into the
accessor) and `_source_package` documents the same first-wins rule.

RED PROOFS, both residuals, against the previous tree (HEAD 9761540, swapped in and
restored): 5 failed / 20 passed before, 25 passed after. The pre-fix symptoms are
concrete — the Browse tree for a map with "" and "   " entries and a blank package
returned titles ['', 'TiviMate', '   ', 'Ghost'] (an empty child, a whitespace child
and a child with no package), and a padded entry produced
source_list ['  TiviMate  ', 'Netflix'] with `_source_package("TiviMate")` returning
None (the resolution miss). After the fix both lists are ['TiviMate', 'Netflix'] and
the lookup answers. The well-formed-map test passes on BOTH trees, which is the
"unchanged for well-formed maps" half of the claim; surviving entries still launch
their key packages (protocol launch list asserted) and the curated fallback list is
untouched (its own test).

Deliberately NOT changed: `_app_name_map` (the raw map behind app_name/source and the
Current App sensor) still returns values as configured, so a padded entry can still
display padded in those two surfaces. A blank value already falls through the
resolve_app_name chain (`if mapped:`), so nothing is broken there, and stripping it
would change sensor.py's output — outside this repair's in-scope paths. Flagged in the
task report as a candidate follow-up rather than done quietly.

Verified: 463 passed / 2 skipped, 464 / 1 with androidtvremote2, ruff clean, drift
engine exit 0 under real HA (23 modules, 58 imports, 164 relative imports, 36 call
arguments, 7 awaited HA calls); the t47/t48 rig (sources, routing, command scripts,
both config-flow suites) is 259 passed.

tests/test_media_sources.py

@@ -108,8 +108,23 @@ class TestSourceList:
         assert player._source_package("   ") is None
 
     def test_every_offered_name_resolves_to_a_package(self, modules):
-        """The invariant the shared directory buys: no name without a destination."""
-        for app_map in (None, {"com.custom.one": "One"}):
+        """The invariant the shared directory buys: no name without a destination.
+
+        t51 extends it to the hand-edited shapes: blanks, padded names and two
+        entries normalizing to one name all still leave only resolvable offers.
+        """
+        for app_map in (
+            None,
+            {"com.custom.one": "One"},
+            {
+                "com.blank": "",
+                "com.blank.package": "   ",
+                TIVIMATE: "  TiviMate  ",
+                "com.a": "Netflix",
+                "com.b": "  Netflix  ",
+                "": "Ghost",
+            },
+        ):
             player, _served = _player(modules, app_map=app_map)
 
             for name in player.source_list:
@@ -256,3 +271,103 @@ class TestAdvertisedFeatures:
 
         assert player.supported_features & MediaPlayerEntityFeature.VOLUME_SET
         assert player.supported_features & MediaPlayerEntityFeature.SELECT_SOURCE
+
+
+class TestNormalizedDirectories:
+    """t51: a hand-edited map is normalized ONCE, in the shared accessor.
+
+    The two residuals t49 left share one cause — `_app_directory` handed the raw map
+    out, so the Browse tree showed a child with a blank title and the reverse lookup
+    compared the user's padded name against itself. The policy now lives in that one
+    accessor (strip names and keys, drop blanks, first-in-map-order wins a shared
+    name) and is pinned here, together with the promise that a well-formed map is
+    untouched.
+    """
+
+    BLANKED = {
+        "com.blank": "",
+        TIVIMATE: "TiviMate",
+        "com.spaces": "   ",
+        "": "Ghost",
+    }
+
+    async def test_a_blank_entry_never_reaches_the_browse_tree(self, modules):
+        """The Browse tree and the dropdown are the same, resolved offer."""
+        player, _served = _player(modules, app_map=dict(self.BLANKED))
+
+        root = await player.async_browse_media()
+
+        assert [child.title for child in root.children] == ["TiviMate"]
+        assert [child.media_content_id for child in root.children] == [TIVIMATE]
+        assert player.source_list == ["TiviMate"]
+
+    async def test_a_blank_package_is_dropped_too(self, modules):
+        """An entry with no package is a child that cannot be launched."""
+        player, _served = _player(
+            modules, app_map={"": "Ghost", "   ": "Ghost 2", TIVIMATE: "TiviMate"}
+        )
+
+        root = await player.async_browse_media()
+
+        assert [child.media_content_id for child in root.children] == [TIVIMATE]
+        assert player.source_list == ["TiviMate"]
+
+    async def test_a_padded_name_is_stripped_once_and_then_resolves(self, modules):
+        player, _served = _player(
+            modules,
+            app_map={TIVIMATE: "  TiviMate  ", "com.netflix.ninja": "Netflix"},
+        )
+
+        root = await player.async_browse_media()
+
+        # display and match key are one string, everywhere
+        assert player.source_list == ["TiviMate", "Netflix"]
+        assert [child.title for child in root.children] == ["TiviMate", "Netflix"]
+        # ...so every spelling the user may type finds the package
+        assert player._source_package("TiviMate") == TIVIMATE
+        assert player._source_package("  TiviMate  ") == TIVIMATE
+        assert player._source_package("tivimate") == TIVIMATE
+
+        await player.async_select_source("TiviMate")
+
+        assert player._manager._protocol.launch_calls == [TIVIMATE]
+
+    async def test_two_packages_with_one_name_keep_a_deterministic_winner(self, modules):
+        """Both apps stay reachable; the NAME goes to the first in map order."""
+        player, _served = _player(
+            modules, app_map={"com.a": "Netflix", "com.b": "  Netflix  "}
+        )
+
+        root = await player.async_browse_media()
+
+        # both are still offered in the tree, each by its own package id
+        assert [(c.media_content_id, c.title) for c in root.children] == [
+            ("com.a", "Netflix"),
+            ("com.b", "Netflix"),
+        ]
+        # the dropdown offers the name once, and resolves to the first entry
+        assert player.source_list == ["Netflix"]
+        assert player._source_package("Netflix") == "com.a"
+
+        await player.async_select_source("Netflix")
+
+        assert player._manager._protocol.launch_calls == ["com.a"]
+
+        # map order decides — the user's order, not chance
+        swapped, _served_swapped = _player(
+            modules, app_map={"com.b": "Netflix", "com.a": "Netflix"}
+        )
+
+        assert swapped._source_package("Netflix") == "com.b"
+
+    async def test_a_wellformed_map_passes_through_unchanged(self, modules):
+        """Stripping touches the EDGES: an inner space is part of the name."""
+        player, _served = _player(
+            modules, app_map={TIVIMATE: "TiviMate Pro", "com.netflix.ninja": "Netflix"}
+        )
+
+        root = await player.async_browse_media()
+
+        assert player.source_list == ["TiviMate Pro", "Netflix"]
+        assert [child.title for child in root.children] == ["TiviMate Pro", "Netflix"]
+        assert player._source_package("TiviMate Pro") == TIVIMATE