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.

install.py

@@ -870,6 +870,47 @@ def detect_frontends(os_type: str, home: Path | None = None) -> list[str]:
     return frontends
 
 
+# The registry's path_exists rules (platforms/_registry.yml install.detect),
+# one row each: (os, platform, path, BIOS directory when it is not the path).
+# The manifests publish them too, but detection runs before any manifest is
+# fetched; a test holds this table equal to the registry. Without it a Linux
+# home holding RetroPie/BIOS or .config/BizHawk/Firmware detected nothing.
+_PATH_RULES: tuple[tuple[str, str, str, str | None], ...] = (
+    ("windows", "retrobat", "C:\\RetroBat\\bios", None),
+    ("windows", "retrobat", "%USERPROFILE%\\RetroBat\\bios", None),
+    ("linux", "emudeck", "$HOME/Emulation/bios", None),
+    ("linux", "retrodeck", "$HOME/.var/app/net.retrodeck.retrodeck", "$HOME/retrodeck"),
+    ("linux", "romm", "/romm/library/bios", None),
+    ("linux", "retropie", "$HOME/RetroPie/BIOS", None),
+    ("windows", "bizhawk", "%USERPROFILE%\\BizHawk\\Firmware", None),
+    ("linux", "bizhawk", "$HOME/.config/BizHawk/Firmware", None),
+    ("linux", "misterfpga", "/media/fat/MiSTer", "/media/fat/games"),
+)
+
+
+def _rule_path(template: str) -> Path:
+    """A rule's path on this machine: $HOME or %USERPROFILE%, then the rest."""
+    bases = (
+        ("$HOME", Path.home()),
+        ("%USERPROFILE%", Path(os.environ.get("USERPROFILE") or Path.home())),
+    )
+    for variable, base in bases:
+        if template.startswith(variable):
+            rest = [part for part in re.split(r"[\\/]", template[len(variable):]) if part]
+            return base.joinpath(*rest)
+    return Path(template)
+
+
+def _detect_by_path(os_type: str, found: list[tuple[str, Path]]) -> None:
+    """Add what a registry path rule finds, for a platform not found yet."""
+    systems = ("linux", "windows") if os_type == "wsl" else (os_type,)
+    for rule_os, platform, path, bios in _PATH_RULES:
+        if rule_os not in systems or any(name == platform for name, _ in found):
+            continue
+        if _rule_path(path).exists():
+            found.append((platform, _rule_path(bios or path)))
+
+
 def detect_platforms(os_type: str) -> list[tuple[str, Path]]:
     """Detect installed emulator platforms and their BIOS directories."""
     found: list[tuple[str, Path]] = []
@@ -981,6 +1022,7 @@ def detect_platforms(os_type: str) -> list[tuple[str, Path]]:
             if system_dir:
                 found.append(("retroarch", system_dir))
 
+    _detect_by_path(os_type, found)
     return found