By inspecting the app menu, I found this solution:
NSApp.sendAction(Selector(("showPreferencesWindow:")), to: nil, from: nil)
I assume that it may not pass App Review for using a private API, though, so less shady alternatives are still welcome.
Update: This has actually passed App Review, so I had marked it as the answer.
Update 2: For a macOS 13 solution, see Manny’s answer.
Update 3: For macOS 14 with SwiftUI, you must use the new SettingsLink view documented here. NSApp.sendAction no longer works.