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.

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AGENTS.md

@@ -5,10 +5,12 @@ executable SwiftPM package, no external dependencies (all Apple frameworks).
 
 ## Architecture
 
-- `Sources/SimpleTopBar/App.swift` — `@main` entry. `MenuBarExtra` with
-  `.menuBarExtraStyle(.window)` hosting `TopBarView`. `AppDelegate` handles the
-  `--self-test` flag and the single-instance guard. `LoginItem` wraps
-  `SMAppService`.
+- `Sources/SimpleTopBar/App.swift` — `@main` entry using a bare
+  `Settings { EmptyView() }` scene, because the app owns its status item
+  manually instead of using `MenuBarExtra`. `AppDelegate.setupStatusItem()`
+  creates the `NSStatusItem`, sets `autosaveName = "SimpleTopBar"`, and shows
+  `TopBarView` inside an `NSPopover`. Handles `--self-test`, `--dump-items`,
+  `--diag`, and the single-instance guard. `LoginItem` wraps `SMAppService`.
 - `Sources/SimpleTopBar/AppListModel.swift` — `@MainActor` `ObservableObject`
   singleton. `refresh()` reads `NSWorkspace.shared.runningApplications` and
   splits them by `activationPolicy` into `regularApps` and `backgroundApps`
@@ -93,6 +95,23 @@ wants it in the final answer every time. Keep it to the cask upgrade commands
 (see the README release section for the exact block), because the app is
 installed through the tap.
 
+## Status item placement (why not MenuBarExtra)
+
+On a full menu bar, a newly created status item is placed leftmost, which on a
+notched MacBook is under the notch and therefore invisible. `MenuBarExtra` gives
+no control over this, so the app creates its own `NSStatusItem` and:
+
+- Sets `autosaveName = "SimpleTopBar"`.
+- On first run, writes `"NSStatusItem Preferred Position SimpleTopBar" = 100`
+  into `UserDefaults.standard`. This private-ish key is what macOS reads to
+  place the item, and 100 lands it at the visible right side. Because it is only
+  written when absent, the user's own ⌘-drag wins and persists via the autosave
+  name.
+
+`--diag` runs full startup and writes every status item's AX position to
+`/tmp/simpletopbar-items.txt`; use it to verify the icon is not under the notch
+(x should be ~1200, not ~765).
+
 ## Gotchas
 
 - `AppListModel` is `@MainActor`; the `NSWorkspace` observers hop back with