Keyboard Manager shortcut remaps become broken after opening the Keyboard Manager settings page until a Ctrl-based remap is triggered

### Microsoft PowerToys version

0.100.0

### Installation method

GitHub

### Area(s) with issue?

Keyboard Manager

### Steps to reproduce

I encountered a reproducible issue with Keyboard Manager shortcut remaps.

Initially, everything worked normally. The problem started after I used the new Keyboard Manager editor. Since then, opening the Keyboard Manager settings page is enough to put shortcut remaps into a broken state.

The issue is reproducible without modifying or saving any mappings.

Minimal reproduction

Mappings:

Alt + X -> Ctrl + W
Ctrl + L -> L

Steps:

Start PowerToys.
Trigger Ctrl + L once.
Verify that Alt + X -> Ctrl + W works normally.
Open PowerToys Settings.
Navigate to Keyboard Manager (no edits or saves required).
Return to another application (for example Notepad).
Test Alt + X again.
Actual behavior
Alt + X no longer works correctly.
Simply opening the Keyboard Manager settings page is sufficient to reproduce the issue.
Triggering the Ctrl + L -> L remap once immediately restores normal behavior.
Opening the Keyboard Manager settings page again immediately breaks it again.
Additional observations
Single-key remaps (for example Caps Lock -> Esc) continue to work correctly.
Pressing Ctrl alone does not fix the issue.
Native shortcuts such as Ctrl + C do not fix the issue.
The problem is only resolved after a Ctrl-based shortcut remap handled by Keyboard Manager itself is triggered.
The issue reproduces with multiple different physical keyboards, so it does not appear to be hardware-specific.
The issue started only after using the new Keyboard Manager editor.
Expected behavior

Opening the Keyboard Manager settings page should not affect runtime shortcut remaps. Shortcut remaps should continue working normally without requiring a Ctrl-based remap to reinitialize them.

### ✔️ Expected Behavior

_No response_

### ❌ Actual Behavior

第一次使用新版 Keyboard Manager 编辑器
│
▼
Shortcut Engine 状态发生异常（持续存在）
│
▼
Alt 类 Shortcut Remap 失效
│
├─────────────► 进入 PowerToys 设置页面
│ │
│ ▼
│ 再次进入异常状态
│
▼
执行一次 Ctrl+L → L（由 Keyboard Manager 处理）
│
▼
Shortcut Engine 状态重新恢复
│
▼
Alt 映射重新正常

### Upload Bug Report ZIP-file

_No response_

### Additional Information

_No response_

### Other Software

_No response_

Start by reproducing the mappings and navigation sequence in the Keyboard Manager settings page, then inspect the shortcut engine state before and after the page is opened. Compare the behavior of the Alt + X and Ctrl + L remaps; done means opening settings no longer disables the Alt-based remap and no Ctrl-based remap is needed to restore it.

Written by the indexing model from the issue text.