Name a root chip after the root, not with its whole path

The chip derivation was TrimEnd(separator), which is a name only for the
Windows drives it was written against: on Unix it made the / chip an empty
pill and the home chip the entire home path, drawn at full width in a header
column nothing bounds. A home directory deep enough — CI's per-job HOME is
forty-six characters — had that one chip walk the header's own buttons out of
the window at the session shell's 472-pixel budget, which is the half of the
runner's red suite the star-column fix before this one did not reach.

A chip says C:, /, ~, or a mount's last segment now; the full path stays on
its command parameter, where length costs nothing. RootChipNameTests pins the
derivation with fixed strings, so it no longer takes a machine with a deep
profile path to ask the question.

src/DodoSSH.Client.Shell/ViewModels/TransfersViewModel.cs

@@ -794,12 +794,48 @@ internal sealed partial class TransfersViewModel : ObservableObject, IAsyncDispo
 
         foreach (var root in LocalDirectory.Roots())
         {
-            LocalRoots.Add(new CrumbViewModel(root.TrimEnd(Path.DirectorySeparatorChar), root));
+            LocalRoots.Add(new CrumbViewModel(RootChipName(root), root));
         }
 
         RefreshLocalCommand.Execute(null);
     }
 
+    /// <summary>What a root's chip in the pane header says: <c>C:</c>, <c>/</c>, <c>~</c>, or a mount's name.</summary>
+    /// <remarks>
+    /// <para>
+    /// A name, never a path — the full path is the chip's <see cref="CrumbViewModel.Path"/> and its command
+    /// parameter, and it stays there. This used to be <c>root.TrimEnd(separator)</c>, which is a name only
+    /// for a Windows drive: on Unix it made the <c>/</c> chip an empty pill and the home chip the entire
+    /// home path, drawn at full width in a header column nothing bounds. A machine whose home directory sat
+    /// deep enough — CI's per-job HOME is forty-six characters — had that one chip push the header's own
+    /// buttons past the window's edge at the session shell's 472-pixel budget.
+    /// </para>
+    /// <para>
+    /// <c>~</c> for home is the one substitution rather than a shortening: every shell a user of this
+    /// application has ever typed into already means "my home directory" by it, which is exactly what the
+    /// chip does when pressed.
+    /// </para>
+    /// </remarks>
+    internal static string RootChipName(string root)
+    {
+        if (string.Equals(root, LocalDirectory.Home, StringComparison.Ordinal))
+        {
+            return "~";
+        }
+
+        var trimmed = root.TrimEnd(Path.DirectorySeparatorChar);
+        if (trimmed.Length == 0)
+        {
+            // Unix's "/": trimming eats the whole string, and the root's name is the root itself.
+            return "/";
+        }
+
+        // A mount under /media or /run/media names itself by its last segment; a Windows drive ("C:") has
+        // no file-name segment at all, and the trimmed root is already the two-character name it always had.
+        var name = Path.GetFileName(trimmed);
+        return name.Length == 0 ? trimmed : name;
+    }
+
     /// <summary>
     /// Gives up the vault, keeping the connection and anything in flight.
     /// </summary>

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

@@ -0,0 +1,47 @@
+using DodoSSH.Client.Shell.ViewModels;
+using DodoSSH.Client.Transfer;
+
+namespace DodoSSH.Client.App.Tests;
+
+/// <summary>What the local pane's root chips are called.</summary>
+/// <remarks>
+/// A chip carries a name and never a path — the path is the chip's command parameter, where its length costs
+/// nothing. The derivation used to be <c>TrimEnd(separator)</c>, which is a name only for a Windows drive:
+/// on Unix it made the <c>/</c> chip an empty pill and the home chip the whole home path, and a home
+/// directory deep enough pushed the pane header's own buttons out of the window — CI's per-job HOME is what
+/// finally said so. These pin the derivation with fixed strings, so the question no longer depends on how
+/// long a path any particular machine keeps its profile under.
+/// </remarks>
+public sealed class RootChipNameTests
+{
+    [Fact]
+    public void TheUnixRootIsASlash_NotAnEmptyPill() =>
+        TransfersViewModel.RootChipName("/").ShouldBe("/");
+
+    /// <remarks>
+    /// The one substitution rather than a shortening: every shell already means "my home directory" by
+    /// <c>~</c>, and the machine's real home path — however deep — stays on the chip's command alone.
+    /// </remarks>
+    [Fact]
+    public void TheHomeChipIsATilde_HoweverDeepHomeSits() =>
+        TransfersViewModel.RootChipName(LocalDirectory.Home).ShouldBe("~");
+
+    [Fact]
+    public void AMountNamesItselfByItsLastSegment() =>
+        TransfersViewModel.RootChipName("/media/usb0").ShouldBe("usb0");
+
+    /// <remarks>
+    /// Windows only, because the input only exists there — <c>LocalDirectory.Roots()</c> produces drive
+    /// roots on no other platform, and <c>Path.GetFileName</c> reads <c>C:\</c> differently on Unix.
+    /// </remarks>
+    [Fact]
+    public void AWindowsDriveKeepsItsTwoCharacterName()
+    {
+        if (!OperatingSystem.IsWindows())
+        {
+            return;
+        }
+
+        TransfersViewModel.RootChipName(@"C:\").ShouldBe("C:");
+    }
+}