Add optional sync between Macs with a shared 8-digit code

Notes and photos were stuck on one machine. A small Go/Postgres backend
stores each group's payload under a code that doubles as the shared
secret, so a second Mac just needs the code — no account or login.

Applying a remote change must not push it straight back, otherwise the
two Macs would bump the version back and forth forever, so payloads are
fingerprinted and identical ones are skipped.

💘 Generated with Crush

Assisted-by: Crush:kimi-k3

Sources/Prompt/App.swift

@@ -19,6 +19,14 @@ final class AppDelegate: NSObject, NSApplicationDelegate {
     func applicationDidFinishLaunching(_ notification: Notification) {
         NSApp.setActivationPolicy(.accessory)
 
+        if CommandLine.arguments.contains("--sync-check") {
+            Task { @MainActor in
+                await SyncService.shared.runDiagnostic()
+                NSApp.terminate(nil)
+            }
+            return
+        }
+
         // Single instance: stale copies keep their hotkeys alive after an
         // update and eat the events meant for the new instance.
         let myPid = ProcessInfo.processInfo.processIdentifier
@@ -43,6 +51,7 @@ final class AppDelegate: NSObject, NSApplicationDelegate {
         // Show the panel on launch so the app is discoverable (it has no Dock
         // icon and the menu bar icon can be hard to spot on a full bar).
         Task { @MainActor in
+            SyncService.shared.start()
             PanelController.shared.show()
         }
     }