CmdPal: Transparent window (#45159)

## Summary

This PR adds:
- Backdrop material customization
  - Alongside acrylic, the following options are now available:
  - Transparent background
  - Mica background
- Background material opacity
  - Lets you control how transparent the background is

## Pictures? Pictures!

<img width="1491" height="928" alt="image"
src="https://github.com/user-attachments/assets/ff4e9e06-fcf1-4f05-bc0a-fb70dc4f39be"
/>



https://github.com/user-attachments/assets/84e83279-afab-481e-b904-f054318c5d2f

<img width="977" height="628" alt="image"
src="https://github.com/user-attachments/assets/241a228d-af3f-448a-94a6-0a282218bd8c"
/>


## PR Checklist

- [x] Closes: #44197
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issues) -->
- [ ] **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/Microsoft.CmdPal.UI.ViewModels/BackdropStyleConfig.cs

@@ -0,0 +1,77 @@
+// Copyright (c) Microsoft Corporation
+// The Microsoft Corporation licenses this file to you under the MIT license.
+// See the LICENSE file in the project root for more information.
+
+namespace Microsoft.CmdPal.UI.ViewModels;
+
+/// <summary>
+/// Configuration parameters for a backdrop style.
+/// </summary>
+public sealed record BackdropStyleConfig
+{
+    /// <summary>
+    /// Gets the type of system backdrop controller to use.
+    /// </summary>
+    public required BackdropControllerKind ControllerKind { get; init; }
+
+    /// <summary>
+    /// Gets the base tint opacity before user adjustments.
+    /// </summary>
+    public required float BaseTintOpacity { get; init; }
+
+    /// <summary>
+    /// Gets the base luminosity opacity before user adjustments.
+    /// </summary>
+    public required float BaseLuminosityOpacity { get; init; }
+
+    /// <summary>
+    /// Gets the brush type to use for preview approximation.
+    /// </summary>
+    public required PreviewBrushKind PreviewBrush { get; init; }
+
+    /// <summary>
+    /// Gets the fixed opacity for styles that don't support user adjustment (e.g., Mica).
+    /// When <see cref="SupportsOpacity"/> is false, this value is used as the effective opacity.
+    /// </summary>
+    public float FixedOpacity { get; init; }
+
+    /// <summary>
+    /// Gets whether this backdrop style supports custom colorization (tint colors).
+    /// </summary>
+    public bool SupportsColorization { get; init; } = true;
+
+    /// <summary>
+    /// Gets whether this backdrop style supports custom background images.
+    /// </summary>
+    public bool SupportsBackgroundImage { get; init; } = true;
+
+    /// <summary>
+    /// Gets whether this backdrop style supports opacity adjustment.
+    /// </summary>
+    public bool SupportsOpacity { get; init; } = true;
+
+    /// <summary>
+    /// Computes the effective tint opacity based on this style's configuration.
+    /// </summary>
+    /// <param name="userOpacity">User's backdrop opacity setting (0-1 normalized).</param>
+    /// <param name="baseTintOpacityOverride">Optional override for base tint opacity (used by colorful theme).</param>
+    /// <returns>The effective opacity to apply.</returns>
+    public float ComputeEffectiveOpacity(float userOpacity, float? baseTintOpacityOverride = null)
+    {
+        // For styles that don't support opacity (Mica), use FixedOpacity
+        if (!SupportsOpacity && FixedOpacity > 0)
+        {
+            return FixedOpacity;
+        }
+
+        // For Solid: only user opacity matters (controls alpha of solid color)
+        if (ControllerKind == BackdropControllerKind.Solid)
+        {
+            return userOpacity;
+        }
+
+        // For blur effects: multiply base opacity with user opacity
+        var baseTint = baseTintOpacityOverride ?? BaseTintOpacity;
+        return baseTint * userOpacity;
+    }
+}