CmdPal: Add filter by Terminal channel (#41582)

## Summary of the Pull Request

- Introduces a new filter on the Profiles page to filter by Terminal
channel.
- Adds a new option to remember the last select Terminal channel (or
automatically reset to All Channels).
- Adds new classes `AppSettings` and `AppSettingsManager` to hold
non-user settings.

Pictures? Pictures!

<img width="1485" height="931" alt="image"
src="https://github.com/user-attachments/assets/2cec7a8d-efe6-4692-a7ba-9608fb181624"
/>

<img width="1730" height="1014" alt="image"
src="https://github.com/user-attachments/assets/87984b82-e085-42a5-b71c-5ddc71ff52ec"
/>

<img width="1722" height="1063" alt="image"
src="https://github.com/user-attachments/assets/97baff23-3db0-404b-8a8d-622f841b344b"
/>

<!-- Please review the items on the PR checklist before submitting-->
## PR Checklist

- [x] Closes: #41432 
- [ ] **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/Properties/Resources.Designer.cs

@@ -60,6 +60,15 @@ namespace Microsoft.CmdPal.Ext.WindowsTerminal.Properties {
             }
         }
         
+        /// <summary>
+        ///   Looks up a localized string similar to All channels.
+        /// </summary>
+        internal static string all_channels {
+            get {
+                return ResourceManager.GetString("all_channels", resourceCulture);
+            }
+        }
+        
         /// <summary>
         ///   Looks up a localized string similar to Windows Terminal Profiles.
         /// </summary>
@@ -132,6 +141,24 @@ namespace Microsoft.CmdPal.Ext.WindowsTerminal.Properties {
             }
         }
         
+        /// <summary>
+        ///   Looks up a localized string similar to Preferred channel.
+        /// </summary>
+        internal static string preferred_channel {
+            get {
+                return ResourceManager.GetString("preferred_channel", resourceCulture);
+            }
+        }
+        
+        /// <summary>
+        ///   Looks up a localized string similar to Preferred channel.
+        /// </summary>
+        internal static string preferred_channel_description {
+            get {
+                return ResourceManager.GetString("preferred_channel_description", resourceCulture);
+            }
+        }
+        
         /// <summary>
         ///   Looks up a localized string similar to Windows Terminal Profiles.
         /// </summary>
@@ -159,6 +186,24 @@ namespace Microsoft.CmdPal.Ext.WindowsTerminal.Properties {
             }
         }
         
+        /// <summary>
+        ///   Looks up a localized string similar to Keep last channel filter.
+        /// </summary>
+        internal static string save_last_selected_channel {
+            get {
+                return ResourceManager.GetString("save_last_selected_channel", resourceCulture);
+            }
+        }
+        
+        /// <summary>
+        ///   Looks up a localized string similar to Remember the last selected channel instead of resetting to All Channels..
+        /// </summary>
+        internal static string save_last_selected_channel_description {
+            get {
+                return ResourceManager.GetString("save_last_selected_channel_description", resourceCulture);
+            }
+        }
+        
         /// <summary>
         ///   Looks up a localized string similar to Settings.
         /// </summary>