[Bug]: When OpenLogi is running all mice stop registering Mouse 4 and 5 in games

### Pre-flight checklist

- [x] I searched [existing issues](https://github.com/AprilNEA/OpenLogi/issues?q=is%3Aissue) and this is not a duplicate.
- [x] I am on the [latest release](https://github.com/AprilNEA/OpenLogi/releases/latest) or a recent `master` build.
- [x] I quit **Logi Options+** before running OpenLogi (the two apps fight over HID++ access and only one can own a receiver at a time).

### Which part of OpenLogi?

Not sure

### OpenLogi version

0.7.4

### Operating system

Windows

### OS version & architecture

Win 11 25H2

### Device model

N/A

### How is the device connected?

Logi Bolt receiver

### Affected area(s)

- [ ] Device discovery / detection
- [ ] Button remapping
- [ ] DPI control
- [ ] SmartShift
- [ ] Per-application profiles
- [ ] Battery status
- [ ] Settings / configuration (TOML)
- [ ] Auto-update
- [ ] Menu bar / tray
- [x] Other

### What happened?

When OpenLogi is running all mice stop registering Mouse 4 and 5 in games. "Backward" and "forward" work but games need raw mouse 4/5 to bind them and work. Not sure if this is also the case in other apps. When I quit OpenLogi, everything works correctly.

### Steps to reproduce

1. Have OpenLogi open.
2. Try to bind/use mouse btn 4/5 in a mouse that is available on including logitech mice (I have the MX Master 4)

### Diagnostics report

```markdown

```

### `openlogi list` output

```text

```

### Logs

```shell

```

### macOS permissions (if applicable)

- [ ] OpenLogi has **Accessibility** permission (needed to remap buttons via the event tap).
- [ ] OpenLogi has **Input Monitoring** permission (needed for Bluetooth-direct devices and capture).

Reproduce the issue on Windows 11 with a Logi Bolt receiver and MX Master 4 while OpenLogi is running, then inspect the mouse input and button-event handling paths. The issue provides no diagnostics, logs, or file names; done means Mouse 4 and 5 remain available for raw binding in games without disabling OpenLogi.

Written by the indexing model from the issue text.