A macOS menu-bar app builds a menu and shows it when its status item is clicked.
Nothing happens on click — the menu never appears. The app is otherwise running.

private func buildStatusItem() {
    statusItem = NSStatusBar.system.statusItem(withLength: NSStatusItem.variableLength)
    statusItem.button?.image = NSImage(systemSymbolName: "star", accessibilityDescription: nil)
    statusItem.button?.action = #selector(statusClicked)
    statusItem.button?.target = self
    statusItem.button?.sendAction(on: [.leftMouseUp, .rightMouseUp])
}

@objc private func statusClicked() {
    if let event = NSApp.currentEvent, event.type == .rightMouseUp {
        showMenu()
    } else {
        togglePanel()
    }
}

private func showMenu() {
    let menu = NSMenu()
    menu.addItem(withTitle: "Open", action: #selector(open), keyEquivalent: "")
    menu.addItem(withTitle: "Quit", action: #selector(NSApplication.terminate(_:)), keyEquivalent: "q")
    statusItem.menu = menu
    statusItem.button?.performClick(nil)
    statusItem.menu = nil
}