fix(installer): unbreak the update path and cache the download

Every update failed at "Could not replace the existing files": the app
relaunches the installer via ShellExecute without a working directory, so
it inherited the app's CWD - which the Start Menu shortcut sets to
<InstallDir>\app. A process's current directory is locked by Windows, so
the installer blocked its own `app` -> `app.bak` rename. Retries and
reboots could not help.

- installer moves its CWD to %TEMP% at startup, and both relaunch sites
  in the UI pass an explicit WorkingDirectory
- cache the release zip in %TEMP%\ClaudeDo-download-cache and reuse it on
  a retry while its SHA-256 still matches, so a failed attempt no longer
  costs another full download; drop it after a successful install, delete
  a mismatching one, prune zips of other versions
- roll back a half-done stash: a leftover app.bak was deleted as a stale
  stash on the next attempt, and that copy was the only one left
- name the blocked path in the error message

src/ClaudeDo.Ui/ViewModels/IslandsShellViewModel.cs

@@ -496,7 +496,13 @@ public sealed partial class IslandsShellViewModel : ViewModelBase, IDisposable
 
         try
         {
-            System.Diagnostics.Process.Start(new System.Diagnostics.ProcessStartInfo(path) { UseShellExecute = true });
+            // WorkingDirectory must NOT stay empty: the child would inherit ours (<InstallDir>\app)
+            // and its locked current directory blocks the installer's own app\ rename.
+            System.Diagnostics.Process.Start(new System.Diagnostics.ProcessStartInfo(path)
+            {
+                UseShellExecute = true,
+                WorkingDirectory = System.IO.Path.GetTempPath(),
+            });
             Environment.Exit(0);
         }
         catch

src/ClaudeDo.Ui/ViewModels/Modals/WorkerConnectionModalViewModel.cs

@@ -1,5 +1,6 @@
 using System;
 using System.Diagnostics;
+using System.IO;
 using ClaudeDo.Ui.Services;
 using CommunityToolkit.Mvvm.Input;
 
@@ -37,7 +38,13 @@ public sealed partial class WorkerConnectionModalViewModel : ViewModelBase
         if (path is null) return;
         try
         {
-            Process.Start(new ProcessStartInfo(path) { UseShellExecute = true });
+            // See IslandsShellViewModel.UpdateNow: an inherited CWD inside the install dir
+            // makes the installer block its own app\ rename.
+            Process.Start(new ProcessStartInfo(path)
+            {
+                UseShellExecute = true,
+                WorkingDirectory = Path.GetTempPath(),
+            });
             Environment.Exit(0);
         }
         catch { /* nothing useful to show */ }