CmdPal: Make settings and app state immutable (#46451)

## Summary
 
 This PR refactors CmdPal settings/state to be immutable end-to-end.
 
 ### Core changes
 - Convert model types to immutable records / init-only properties:
   - `SettingsModel`
   - `AppStateModel`
   - `ProviderSettings`
   - `DockSettings`
   - `RecentCommandsManager`
- supporting settings types (fallback/hotkey/alias/top-level
hotkey/history items, etc.)
- Replace mutable collections with immutable equivalents where
appropriate:
   - `ImmutableDictionary<,>`
   - `ImmutableList<>`
 - Move mutation flow to atomic service updates:
- `ISettingsService.UpdateSettings(Func<SettingsModel, SettingsModel>)`
   - `IAppStateService.UpdateState(Func<AppStateModel, AppStateModel>)`
- Update ViewModels/managers/services to use copy-on-write (`with`)
patterns instead of in-place
mutation.
- Update serialization context + tests for immutable model graph
compatibility.
 
 ## Why
 
Issue #46437 is caused by mutable shared state being updated from
different execution paths/threads,
leading to race-prone behavior during persistence/serialization.
 
By making settings/app state immutable and using atomic swap/update
patterns, we remove in-place
mutation and eliminate this class of concurrency bug.
 
 ## Validation
 
 - Built successfully:
   - `Microsoft.CmdPal.UI.ViewModels`
   - `Microsoft.CmdPal.UI`
   - `Microsoft.CmdPal.UI.ViewModels.UnitTests`
 - Updated unit tests for immutable update patterns.
 
 Fixes #46437

---------

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

src/modules/cmdpal/Microsoft.CmdPal.UI/MainWindow.xaml.cs

@@ -910,8 +910,7 @@ public sealed partial class MainWindow : WindowEx,
             // the last non-dock placement because dock sessions intentionally skip updates.
             if (_currentWindowPosition.IsSizeValid)
             {
-                settings.LastWindowPosition = _currentWindowPosition;
-                settingsService.Save();
+                settingsService.UpdateSettings(s => s with { LastWindowPosition = _currentWindowPosition });
             }
         }