Make the menu bar icon visible on a full menu bar

New status items land leftmost, which on a notched Mac lands under the
notch and is invisible, so the app appeared broken. Replace MenuBarExtra
with a managed status item that carries an autosave name and a persisted
preferred position, and add a diagnostic dump to verify placement.

💘 Generated with Crush

Assisted-by: Crush:deepseek-v4.1-flash

Sources/SimpleTopBar/SelfTest.swift

@@ -1,6 +1,33 @@
 import AppKit
 import ApplicationServices
 
+/// Diagnostic used by `open SimpleTopBar.app --args --dump-items`. Writes the
+/// live Accessibility view of the menu bar to /tmp so it can be inspected
+/// without a GUI, then exits.
+func dumpMenuBarItems() {
+    var lines: [String] = []
+    lines.append("bundle=\(Bundle.main.bundleIdentifier ?? "?")")
+    lines.append("authorized=\(AXIsProcessTrusted())")
+    let items = MenuBarItemManager.enumerate()
+    lines.append("count=\(items.count)")
+    for item in items {
+        let pos = MenuBarItemManager.pointAttribute(item.element, kAXPositionAttribute)
+        lines.append("\(item.appName) | \(item.title) | pid=\(item.pid) | id=\(item.id) | pos=\(pos.map { "\(Int($0.x)),\(Int($0.y))" } ?? "?")")
+    }
+    let own = MenuBarItemManager.enumerate(includeOwn: true).filter {
+        $0.pid == ProcessInfo.processInfo.processIdentifier
+    }
+    lines.append("own-status-items=\(own.count)")
+    for item in own {
+        let pos = MenuBarItemManager.pointAttribute(item.element, kAXPositionAttribute)
+        lines.append("OWN \(item.appName) | \(item.title) | id=\(item.id) | pos=\(pos.map { "\(Int($0.x)),\(Int($0.y))" } ?? "?")")
+    }
+    let text = lines.joined(separator: "\n")
+    try? text.write(toFile: "/tmp/simpletopbar-items.txt", atomically: true, encoding: .utf8)
+    print(text)
+    exit(0)
+}
+
 /// Headless verification for `swift run SimpleTopBar --self-test`.
 /// Exercises the background-app overflow helpers and reports the live split
 /// between regular and background applications, then exits 0/1.