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

<!-- Provide a more detailed description of the PR, other things fixed,
or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

<!-- Describe how you validated the behavior. Add automated tests
wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed

src/modules/cmdpal/ext/Microsoft.CmdPal.Ext.WindowsTerminal/Commands/LaunchProfileAsAdminCommand.cs

@@ -20,13 +20,15 @@ internal sealed partial class LaunchProfileAsAdminCommand : InvokableCommand
     private readonly string _profile;
     private readonly bool _openNewTab;
     private readonly bool _openQuake;
+    private readonly AppSettingsManager _appSettingsManager;
 
-    internal LaunchProfileAsAdminCommand(string id, string profile, bool openNewTab, bool openQuake)
+    internal LaunchProfileAsAdminCommand(string id, string profile, bool openNewTab, bool openQuake, AppSettingsManager appSettingsManager)
     {
         this._id = id;
         this._profile = profile;
         this._openNewTab = openNewTab;
         this._openQuake = openQuake;
+        this._appSettingsManager = appSettingsManager;
 
         this.Name = Resources.launch_profile_as_admin;
         this.Icon = Icons.AdminIcon;
@@ -59,6 +61,17 @@ internal sealed partial class LaunchProfileAsAdminCommand : InvokableCommand
             //_context.API.ShowMsg(name, message, string.Empty);
             Logger.LogError($"Failed to open Windows Terminal: {ex.Message}");
         }
+
+        try
+        {
+            _appSettingsManager.Current.AddRecentlyUsedProfile(id, profile);
+            _appSettingsManager.Save();
+        }
+        catch (Exception ex)
+        {
+            // We don't want to fail the whole operation if we can't save the recently used profile
+            Logger.LogError($"Failed to save recently used profile: {ex.Message}");
+        }
     }
 #pragma warning restore IDE0059, CS0168, SA1005
 

src/modules/cmdpal/ext/Microsoft.CmdPal.Ext.WindowsTerminal/Commands/LaunchProfileCommand.cs

@@ -20,13 +20,15 @@ internal sealed partial class LaunchProfileCommand : InvokableCommand
     private readonly string _profile;
     private readonly bool _openNewTab;
     private readonly bool _openQuake;
+    private readonly AppSettingsManager _appSettingsManager;
 
-    internal LaunchProfileCommand(string id, string profile, string iconPath, bool openNewTab, bool openQuake)
+    internal LaunchProfileCommand(string id, string profile, string iconPath, bool openNewTab, bool openQuake, AppSettingsManager appSettingsManager)
     {
         this._id = id;
         this._profile = profile;
         this._openNewTab = openNewTab;
         this._openQuake = openQuake;
+        this._appSettingsManager = appSettingsManager;
 
         this.Name = Resources.launch_profile;
         this.Icon = new IconInfo(iconPath);
@@ -62,6 +64,17 @@ internal sealed partial class LaunchProfileCommand : InvokableCommand
             // _context.API.ShowMsg(name, message, string.Empty);
             Logger.LogError($"Failed to open Windows Terminal: {ex.Message}");
         }
+
+        try
+        {
+            _appSettingsManager.Current.AddRecentlyUsedProfile(id, profile);
+            _appSettingsManager.Save();
+        }
+        catch (Exception ex)
+        {
+            // We don't want to fail the whole operation if we can't save the recently used profile
+            Logger.LogError($"Failed to save recently used profile: {ex.Message}");
+        }
     }
 #pragma warning restore IDE0059, CS0168