Add support for filterable, nested context menus (#38776)

_targets #38573_

At first I just wanted to add support for nested context menus.

But then I also had to add a search box, so the focus wouldn't get weird.

End result:

![nested-menus-001](https://github.com/user-attachments/assets/4e8f1ec8-4b09-4095-9b81-caf7abde8aea)

This gets rid of the need to have the search box and the command bar both track item keybindings - now it's just in the command bar.

Closes #38299
Closes #38442

src/modules/cmdpal/Microsoft.CmdPal.UI.ViewModels/Messages/TryCommandKeybindingMessage.cs

@@ -2,8 +2,11 @@
 // The Microsoft Corporation licenses this file to you under the MIT license.
 // See the LICENSE file in the project root for more information.
 
-using Microsoft.CommandPalette.Extensions;
+using Windows.System;
 
 namespace Microsoft.CmdPal.UI.ViewModels.Messages;
 
-public record UpdateItemKeybindingsMessage(Dictionary<KeyChord, CommandContextItemViewModel>? Keys);
+public record TryCommandKeybindingMessage(bool Ctrl, bool Alt, bool Shift, bool Win, VirtualKey Key)
+{
+    public bool Handled { get; set; }
+}

src/modules/cmdpal/Microsoft.CmdPal.UI.ViewModels/Messages/UpdateCommandBarMessage.cs

@@ -3,6 +3,7 @@
 // See the LICENSE file in the project root for more information.
 
 using System.ComponentModel;
+using Microsoft.CommandPalette.Extensions;
 
 namespace Microsoft.CmdPal.UI.ViewModels.Messages;
 
@@ -13,22 +14,42 @@ public record UpdateCommandBarMessage(ICommandBarContext? ViewModel)
 {
 }
 
-// Represents everything the command bar needs to know about to show command
-// buttons at the bottom.
-//
-// This is implemented by both ListItemViewModel and ContentPageViewModel,
-// the two things with sub-commands.
-public interface ICommandBarContext : INotifyPropertyChanged
+public interface IContextMenuContext : INotifyPropertyChanged
 {
     public IEnumerable<CommandContextItemViewModel> MoreCommands { get; }
 
     public bool HasMoreCommands { get; }
 
+    public List<CommandContextItemViewModel> AllCommands { get; }
+
+    /// <summary>
+    /// Generates a mapping of key -> command item for this particular item's
+    /// MoreCommands. (This won't include the primary Command, but it will
+    /// include the secondary one). This map can be used to quickly check if a
+    /// shortcut key was pressed
+    /// </summary>
+    /// <returns>a dictionary of KeyChord -> Context commands, for all commands
+    /// that have a shortcut key set.</returns>
+    public Dictionary<KeyChord, CommandContextItemViewModel> Keybindings()
+    {
+        return MoreCommands
+            .Where(c => c.HasRequestedShortcut)
+            .ToDictionary(
+            c => c.RequestedShortcut ?? new KeyChord(0, 0, 0),
+            c => c);
+    }
+}
+
+// Represents everything the command bar needs to know about to show command
+// buttons at the bottom.
+//
+// This is implemented by both ListItemViewModel and ContentPageViewModel,
+// the two things with sub-commands.
+public interface ICommandBarContext : IContextMenuContext
+{
     public string SecondaryCommandName { get; }
 
     public CommandItemViewModel? PrimaryCommand { get; }
 
     public CommandItemViewModel? SecondaryCommand { get; }
-
-    public List<CommandContextItemViewModel> AllCommands { get; }
 }