CmdPal: Add option to choose default order for Terminal profiles (#41945)

## Summary of the Pull Request

This PR adds a new drop-down to the Windows Terminal extension settings
page that allows the user to choose the default sort order of profiles.
The available options are:
- Default (currently alphabetical, but may change in the future)
- Alphabetical
- Most recently used

It also extends the app data to store AppSettings, including a list of
up to 64 recently used profiles, stored as pairs of profile name and
terminal app ID.

Pictures? Pictures!

<img width="1821" height="1097" alt="image"
src="https://github.com/user-attachments/assets/c751dcbf-e638-4207-a3e4-6dd283c5239c"
/>

<img width="1694" height="521" alt="image"
src="https://github.com/user-attachments/assets/914c0498-98fa-4ed7-997d-f988253c923c"
/>

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## PR Checklist

- [x] Closes: #41430 
- [ ] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [ ] **Tests:** Added/updated and all pass
- [ ] **Localization:** All end-user-facing strings can be localized
- [ ] **Dev docs:** Added/updated
- [ ] **New binaries:** Added on the required places
- [ ] [JSON for
signing](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ESRPSigning_core.json)
for new binaries
- [ ] [WXS for
installer](https://github.com/microsoft/PowerToys/blob/main/installer/PowerToysSetup/Product.wxs)
for new binaries and localization folder
- [ ] [YML for CI
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ci/templates/build-powertoys-steps.yml)
for new test projects
- [ ] [YML for signed
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/release.yml)
- [ ] **Documentation updated:** If checked, please file a pull request
on [our docs
repo](https://github.com/MicrosoftDocs/windows-uwp/tree/docs/hub/powertoys)
and link it here: #xxx

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or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

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wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed

src/modules/cmdpal/ext/Microsoft.CmdPal.Ext.WindowsTerminal/Pages/ProfilesListPage.cs

@@ -51,9 +51,16 @@ internal sealed partial class ProfilesListPage : ListPage, INotifyItemsChanged
         Icon = Icons.TerminalIcon;
         Name = Resources.profiles_list_page_name;
         _terminalSettings = terminalSettings;
+        _terminalSettings.Settings.SettingsChanged += Settings_SettingsChanged;
         _appSettingsManager = appSettingsManager;
     }
 
+    private void Settings_SettingsChanged(object sender, Settings args)
+    {
+        EnsureInitialized();
+        RaiseItemsChanged();
+    }
+
     private List<ListItem> Query()
     {
         EnsureInitialized();
@@ -62,7 +69,27 @@ internal sealed partial class ProfilesListPage : ListPage, INotifyItemsChanged
         openNewTab = _terminalSettings.OpenNewTab;
         openQuake = _terminalSettings.OpenQuake;
 
-        var profiles = _terminalQuery.GetProfiles();
+        var profiles = _terminalQuery.GetProfiles()!;
+
+        switch (_terminalSettings.ProfileSortOrder)
+        {
+            case ProfileSortOrder.MostRecentlyUsed:
+                var mru = _appSettingsManager.Current.RecentlyUsedProfiles ?? [];
+                profiles = profiles.OrderBy(p =>
+                    {
+                        var key = new TerminalProfileKey(p.Terminal?.AppUserModelId ?? string.Empty, p.Name ?? string.Empty);
+                        var index = mru.IndexOf(key);
+                        return index == -1 ? int.MaxValue : index;
+                    })
+                    .ThenBy(static p => p.Name, StringComparer.CurrentCultureIgnoreCase)
+                    .ToList();
+                break;
+            case ProfileSortOrder.Default:
+            case ProfileSortOrder.Alphabetical:
+            default:
+                profiles = profiles.OrderBy(static p => p.Name, StringComparer.CurrentCultureIgnoreCase);
+                break;
+        }
 
         if (terminalFilters?.IsAllSelected == false)
         {
@@ -78,12 +105,12 @@ internal sealed partial class ProfilesListPage : ListPage, INotifyItemsChanged
                 continue;
             }
 
-            result.Add(new ListItem(new LaunchProfileCommand(profile.Terminal.AppUserModelId, profile.Name, profile.Terminal.LogoPath, openNewTab, openQuake))
+            result.Add(new ListItem(new LaunchProfileCommand(profile.Terminal.AppUserModelId, profile.Name, profile.Terminal.LogoPath, openNewTab, openQuake, _appSettingsManager))
             {
                 Title = profile.Name,
                 Subtitle = profile.Terminal.DisplayName,
                 MoreCommands = [
-                    new CommandContextItem(new LaunchProfileAsAdminCommand(profile.Terminal.AppUserModelId, profile.Name, openNewTab, openQuake)),
+                    new CommandContextItem(new LaunchProfileAsAdminCommand(profile.Terminal.AppUserModelId, profile.Name, openNewTab, openQuake, _appSettingsManager)),
                 ],
             });
         }