Let a closed terminal take its own status line with it

The strip along the bottom is one line for the whole window, and connecting
writes to it, so "Connected to prod-db." outlived the tab it was about: close
prod-db, look at the terminal beside it, and the bar was still reporting on a
session that is no longer there.

A connection's own lines are now owned by the attempt that wrote them, and
closing a tab clears the line only when that is what the bar is holding.
Ownership rather than a blanket clear on close, because the alternative loses
the sentences this bar exists for — a failed save or a refused sync is what the
design deleted the bar's other four fields to make room for, and closing a
terminal is no answer to one.

tests/DodoSSH.Client.App.Tests/ShellFlowTests.cs

@@ -1254,6 +1254,68 @@ public sealed class ShellFlowTests : IAsyncLifetime
         shell.IsTerminalShowing.ShouldBeTrue();
     }
 
+    /// <remarks>
+    /// The status line is one line for the whole window, so a sentence about a session that has been closed is
+    /// a sentence the user reads over some other terminal.
+    /// </remarks>
+    [Fact]
+    public async Task ClosingATab_TakesItsOwnStatusLineWithIt()
+    {
+        var vault = await ReadyToConnectAsync();
+
+        await using var renderer = await FakeRenderer.AttachAsync(workspace, Token);
+
+        await vault.ConnectCommand.ExecuteAsync(null);
+        vault.Status.ShouldContain("Connected", Case.Insensitive);
+
+        await shell.CloseTabCommand.ExecuteAsync(shell.Tabs[0]);
+
+        vault.Status.ShouldBeEmpty();
+    }
+
+    /// <remarks>
+    /// The other half, and the reason closing does not simply blank the bar: everything this application has
+    /// to say about a save, a sync or a refusal goes through the same line — see <c>StatusBar.axaml</c> — and
+    /// closing a terminal answers none of it.
+    /// </remarks>
+    [Fact]
+    public async Task ClosingATab_LeavesAStatusLineThatIsAboutSomethingElse()
+    {
+        var vault = await ReadyToConnectAsync();
+
+        await using var renderer = await FakeRenderer.AttachAsync(workspace, Token);
+
+        await vault.ConnectCommand.ExecuteAsync(null);
+        vault.Status = "The keychain could not be saved.";
+
+        await shell.CloseTabCommand.ExecuteAsync(shell.Tabs[0]);
+
+        vault.Status.ShouldBe("The keychain could not be saved.");
+    }
+
+    /// <remarks>
+    /// Two sessions to the same host, which is the case a label could not tell apart: the line belongs to the
+    /// attempt that wrote it, so closing the other one leaves it alone.
+    /// </remarks>
+    [Fact]
+    public async Task ClosingATab_LeavesTheLineAnotherTabWrote()
+    {
+        var vault = await ReadyToConnectAsync();
+
+        await using var renderer = await FakeRenderer.AttachAsync(workspace, Token);
+
+        await vault.ConnectCommand.ExecuteAsync(null);
+        var first = shell.Tabs[0];
+
+        // The second connection's own line is what the bar holds now.
+        await vault.ConnectCommand.ExecuteAsync(null);
+        var reported = vault.Status;
+
+        await shell.CloseTabCommand.ExecuteAsync(first);
+
+        vault.Status.ShouldBe(reported);
+    }
+
     // ---- Connecting, while it is still happening ----
     //
     // A handshake is a network round trip and no longer holds the vault while it runs, so there is a stretch