fix: detect platforms the registry describes

The registry declares where each platform keeps its BIOS and every
manifest publishes it, but the installer detects before it fetches
any manifest and never had RetroPie, BizHawk, RetroBat's paths, or
EmuDeck's default folder. It now carries the registry's path rules,
held equal to the registry by a test.

tests/test_install.py

@@ -920,6 +920,56 @@ class StandaloneCopiesReadWhereThePackPutTheFile(unittest.TestCase):
             install._validate_manifest(manifest, "emudeck")
 
 
+class DetectionFollowsTheRegistry(unittest.TestCase):
+    """The registry declared RetroPie at ~/RetroPie/BIOS and BizHawk at
+    ~/.config/BizHawk/Firmware, every manifest published it, and the
+    installer never read it: such a home detected nothing."""
+
+    def test_the_table_is_the_registry(self):
+        import yaml  # noqa: PLC0415
+
+        registry = yaml.safe_load(
+            (Path(__file__).resolve().parents[1] / "platforms" / "_registry.yml").read_text()
+        )
+        rules = {
+            (rule["os"], name, rule["path"], rule.get("bios_path"))
+            for name, entry in registry["platforms"].items()
+            for rule in (entry.get("install") or {}).get("detect", [])
+            if rule["method"] == "path_exists"
+        }
+        self.assertEqual(set(install._PATH_RULES), rules)
+
+    def _home(self) -> Path:
+        home = Path(_tempdir(self))
+        patcher = unittest.mock.patch.dict(os.environ, {"HOME": str(home), "USERPROFILE": str(home)})
+        patcher.start()
+        self.addCleanup(patcher.stop)
+        return home
+
+    def test_a_home_layout_is_detected(self):
+        home = self._home()
+        (home / "RetroPie" / "BIOS").mkdir(parents=True)
+        (home / ".config" / "BizHawk" / "Firmware").mkdir(parents=True)
+        found: list = []
+        install._detect_by_path("linux", found)
+        self.assertIn(("retropie", home / "RetroPie" / "BIOS"), found)
+        self.assertIn(("bizhawk", home / ".config" / "BizHawk" / "Firmware"), found)
+
+    def test_a_windows_profile_path_is_detected(self):
+        home = self._home()
+        (home / "BizHawk" / "Firmware").mkdir(parents=True)
+        found: list = []
+        install._detect_by_path("windows", found)
+        self.assertEqual(found, [("bizhawk", home / "BizHawk" / "Firmware")])
+
+    def test_a_platform_already_found_is_not_added_again(self):
+        home = self._home()
+        (home / "Emulation" / "bios").mkdir(parents=True)
+        found = [("emudeck", home / "elsewhere" / "bios")]
+        install._detect_by_path("linux", found)
+        self.assertEqual(found, [("emudeck", home / "elsewhere" / "bios")])
+
+
 class InstallerStaysOnPython38AndTheStdlib(unittest.TestCase):
     """install.py runs where the bootstraps let it run: Python 3.8, stdlib only.