feat(installer): replace sync ModeDetector with async InstallModeDetector

Placeholder edit to App.xaml.cs to keep the project building until Task 11
wires the new async detector.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/ClaudeDo.Installer/Core/InstallModeDetector.cs

@@ -0,0 +1,41 @@
+namespace ClaudeDo.Installer.Core;
+
+public sealed record DetectedState(
+    InstallerMode Mode,
+    InstallManifest? Existing,
+    GiteaRelease? LatestRelease,
+    string? LatestVersion);
+
+public sealed class InstallModeDetector
+{
+    private readonly IReleaseClient _releases;
+
+    public InstallModeDetector(IReleaseClient releases)
+    {
+        _releases = releases;
+    }
+
+    public async Task<DetectedState> DetectAsync(string installDir, CancellationToken ct)
+    {
+        var manifest = InstallManifestStore.TryRead(installDir);
+        if (manifest is null)
+            return new DetectedState(InstallerMode.FreshInstall, null, null, null);
+
+        var release = await _releases.GetLatestReleaseAsync(ct);
+        if (release is null)
+            return new DetectedState(InstallerMode.Config, manifest, null, null);
+
+        var latestVersion = release.TagName.TrimStart('v', 'V');
+        if (IsNewer(latestVersion, manifest.Version))
+            return new DetectedState(InstallerMode.Update, manifest, release, latestVersion);
+
+        return new DetectedState(InstallerMode.Config, manifest, release, latestVersion);
+    }
+
+    private static bool IsNewer(string latest, string current)
+    {
+        if (!Version.TryParse(latest, out var lv)) return false;
+        if (!Version.TryParse(current, out var cv)) return false;
+        return lv > cv;
+    }
+}