fix: load persisted capture region at launch; REGION-PERSIST selftest phase

Ben-reported: picker opened on every activation. AppModel.init set region = nil and never
read UserDefaults back; saving worked, every launch forgot it. init now loads via
loadPersistedRegion() (decode + isStillValid). Selftest phase 2 writes a known region,
reloads through the same path, asserts the rect, restores the user's stored value.
Coordinator ran it: PICKER-SELFTEST PASS + REGION-PERSIST PASS, 90/90 tests green.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

Sources/Shotdeck/AppModel.swift

@@ -72,7 +72,7 @@ public final class AppModel {
             captures: [],
             pdfFileName: nil
         )
-        self.region = nil
+        self.region = Self.loadPersistedRegion()
         self.screenRecordingGranted = ScreenCapturer.isScreenRecordingGranted
         // Seeded from FolderSettings.resolve() via resolvedAppSupportPaths — never .standard().
         let folders = FolderSettings.resolve()
@@ -237,6 +237,14 @@ public final class AppModel {
         NSWorkspace.shared.open(url)
     }
 
+    static func loadPersistedRegion() -> CaptureRegion? {
+        guard let data = UserDefaults.standard.data(forKey: CaptureRegion.defaultsKey),
+              let decoded = try? JSONDecoder().decode(CaptureRegion.self, from: data),
+              decoded.isStillValid
+        else { return nil }
+        return decoded
+    }
+
     private func persistRegion(_ picked: CaptureRegion) {
         replaceRegion(picked)
         if let encoded = try? JSONEncoder().encode(picked) {