[Grab and Move] Alt key assigned to mouse side button does not trigger the feature

### Microsoft PowerToys version

0.99.1

### Installation method

Microsoft Store

### Area(s) with issue?

Mouse Utilities

### Steps to reproduce

1. Use a mouse (e.g., Microsoft IntelliMouse) and assign the "Alt" key to a side button using its configuration software.
2. Enable "Grab and Move" in PowerToys settings.
3. Try to drag a window while holding the mouse side button (assigned as Alt).
4. Observe that the window does not move.
5. Perform the same action using the physical Alt key on the keyboard, and observe that it works correctly.

### ✔️ Expected Behavior

The "Grab and Move" feature should trigger and allow window movement even when the Alt key input comes from a remapped mouse side button.

### ❌ Actual Behavior

The feature only responds to physical keyboard input and ignores the Alt key signal sent from the mouse side button.

### Upload Bug Report ZIP-file

_No response_

### Additional Information

_No response_

### Other Software

_No response_

Start by locating the Mouse Utilities Grab and Move entry point and its mouse and keyboard input handling. Reproduce the side-button Alt case and compare it with the physical Alt case; done means Grab and Move moves the window in both cases while existing behavior remains intact.

Written by the indexing model from the issue text.