[Bug]: Mac Brew Installation apparently cannot get Input Monitoring permission

### 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

0.8.1

### Operating system

macOS

### OS version & architecture

MacOS 26.5.2 on Apple Silicon M2 Pro

### Device model

MX Master 3

### How is the device connected?

Bluetooth (direct, no receiver)

### Affected area(s)

- [x] 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 I installed the app via brew --cask, I was unable to enable Input Monitoring permission for OpenLogi, either via automated prompt or manually adding OpenLogi.app to the allow-list. I uninstalled and reinstalled from signed DMG and it worked first try.

I see archived issues #192 and #314 which may be related, but I think are different enough to warrant a new issue.

### Steps to reproduce

1. I fully uninstalled Logi Options+ from the system - no logi-owned processes running in Activity Monitor at all. Then full restart.
2. I installed OpenLogi via brew cask install method.
3. I opened it and it requested Accessibility permissions. Detected my USB-connected camera and light fine. No mouse detected.
4. Clicked "add device" and got an error that input monitoring was not enabled. Clicked "try again." Nothing.
5. Went to input monitoring settings and added OpenLogi manually. Quit and reopened the app. Same error.
6. Went to settings in OpenLogi -> Permissions. Was able to enable every other permission either via normal prompt or via manually adding OpenLogi in system settings, but the Input Monitoring permission was disabled and could not be enabled.
7. Brew remove the cask.
8. Installed the app via DMG from Github. On first open all permissions are enabled without any prompting (presumably a carryover from OpenLogi.app being added manually to all lists).
9. Annoyingly, now deleting the DMG build and reinstalling via brew does show all permissions enabled so I cannot re-enter the broken state to confirm.

### Diagnostics report

```markdown
Working DMG install:

### OpenLogi Diagnostics

**App**
- OpenLogi (GUI): v0.8.1 (release)
- Agent: v0.8.1 (connected)
- IPC protocol: GUI 28 / agent 28
- Inventory: ready
- OS: macOS 26.5.2 (arm64)
- Locale: en-US (UI: follow system)
- Accessibility: granted · Input hook: installed
- Launch at login: no · Menu bar: yes · Update check: on
- Running from: source build (dev)
- Config: schema 6 · 2 configured device(s) · thumbwheel 14

**Assets**
- Source: user cache · Index: loaded (210 models) · User cache: present
- Cache path: ~/.local/share/openlogi/assets · Bundle assets: absent

**Devices (3)**
- MX Master 3 — mouse (codename: Wireless Mouse MX Master 3)
- Connection: Bluetooth (direct) · Online: yes · Battery: 0% (charging, critical)
- Capabilities: buttons=yes, pointer=yes, lighting=no
- Model: 1b023 (model-ids: b023/4082/0000, ext-model: 01)
- Transports: eQuad, BTLE
- Render: mx_master_3 · direct
- Litra Glow — light
- Connection: Wired (USB) · Online: yes · Battery: n/a
- Capabilities: not probed
- Model: raw:c900
- Render: litra_glow · direct
- Logitech Webcam C925e — camera
- Connection: unknown · Online: yes · Battery: n/a
- Capabilities: not probed
- Model: 085b
- Render: c925e · Slot 0

Cannot re-enter the broken state to get diagnostics.
```

### `openlogi list` output

```text
Cannot re-enter the broken state.
```

### Logs

```shell
Cannot re-enter the broken state
```

### macOS permissions (if applicable)

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

Start by reproducing the Homebrew cask installation on macOS and compare its Input Monitoring behavior with the signed GitHub DMG installation. The issue provides no code or test entry point; done means a fresh brew installation can obtain Input Monitoring permission and discover Bluetooth-direct devices.

Written by the indexing model from the issue text.