Record the keep-alive corrections in the port notes and the manual checks

The port doc's backgrounding decision now carries the four corrections
rather than describing a wiring that was not true, and Phase 14 gains
the checks a phone can actually run: a backgrounded shell surviving, an
idle Files connection surviving, the permission ask arriving at the
first thing worth showing, and a refusal costing the notification and
nothing else.

docs/manual-checks.md

@@ -2075,9 +2075,57 @@ Queue several files in each direction, put the phone to sleep with the screen of
 notification goes away when the last one does — with no shell open. With a shell open it stays, because that
 is what it was already for.
 
+Now, separately: open a shell to the host, press the home button (backgrounding rather than sleeping — the
+distinction matters, because backgrounded is the state in which Android is free to kill a process no
+foreground service is protecting), wait thirty seconds with the shell doing nothing, and return.
+
+**Pass:** the notification stayed up the whole time, and the shell is exactly where it was — same scrollback,
+same prompt — with typing reaching the host immediately. Exit the shell.
+
+**Pass:** the notification goes with it, once nothing else is open.
+
 **Failure means:** an upload that stalls with the screen off is the count not reaching
 `SessionForegroundService`, and Android has stopped the process mid-transfer. A notification left up
-afterwards is `ActivityChanged` not being subscribed — the other end of the same wire.
+afterwards is `ActivityChanged` not being subscribed — the other end of the same wire. A shell that has
+disconnected on return is `MainWindowViewModel.TerminalSessionOpened` never reaching `SessionKeepAlive` — the
+service only ever heard about a shell *ending*, so it never came up for one in the first place.
+
+### 14.6a A Files connection with nothing moving still survives backgrounding
+
+Connect to a host on the Files screen with no transfer queued — just browse to somewhere and stop. Note the
+directory shown, then background the app, wait thirty seconds, and return.
+
+**Pass:** the notification stayed up the whole time (check the shade if the return is too quick to see it
+directly), and the pane is exactly where it was — the same listing, the same breadcrumb — with no reconnect
+needed.
+
+**Failure means:** `TransfersViewModel.HasLiveFileSession` not reaching `SessionKeepAlive`, so an idle but
+still-open SFTP connection read as nothing running at all and the process was free to die under it.
+
+### 14.6b The notification permission is asked for once, at the first thing worth showing · **needs Android 13+**
+
+On a device running Android 13 or later, on a fresh install that has never connected to anything, open a
+shell or the Files screen for the first time.
+
+**Pass:** a system dialogue asking to allow notifications appears at that moment — not at launch, and not
+before this first connect. Answer it either way; the connection completes regardless, and background the app
+afterwards to confirm nothing else changed about it.
+
+**Failure means:** the dialogue appearing at launch is asking before there is anything on screen to justify
+it. Never appearing at all on API 33+ is the harder failure to notice, because nothing else surfaces it —
+the service still starts and still holds the process open, only the receipt is invisible. See
+`SessionForegroundService.RequestNotificationPermission`.
+
+### 14.6c Refusing the permission costs the notification and nothing else
+
+Continuing from 14.6b: choose **Don't allow** on the system dialogue. Queue a transfer, or open a shell, and
+background the app.
+
+**Pass:** no notification appears anywhere, but the transfer still finishes, or the shell is still there on
+return, exactly as in 14.1–14.6a.
+
+**Failure means:** anything disconnecting or failing here is the permission refusal being read as though it
+had refused the service itself, rather than only the notification Android draws for it.
 
 ### 14.7 SAVE FILE writes where you pointed it, and the file opens