[Bug]: Function-key mapping is positionally offset from the physical keyboard layout

### 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?

GUI (desktop app)

### OpenLogi version

0.7.1

### Operating system

macOS

### OS version & architecture

macOS 26.6.2, Apple Silicon M4

### Device model

MX Mechanical Mini for Mac

### How is the device connected?

Bluetooth (direct, no receiver)

### Affected area(s)

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

### What happened?

The logical F-key indices are incorrectly mapped to physical key positions. The overlay labels themselves are correct, but their target coordinates/key indices are shifted, causing F1, F2, etc. to reference the wrong keys.

### Steps to reproduce

1. Open the keyboard configuration/mapping screen for the Logitech keyboard shown.
2. Select or view the **F-key mapping** layer.
3. Enable/display the mapping overlay that connects logical F-keys to the physical keys.
4. Inspect the connector lines between the F-key labels and the keyboard.
5. Observe that the logical keys are mapped to incorrect physical positions—for example, **F1 points to the physical F4 key** instead of F1.
6. Compare the remaining F-key mappings; multiple mappings are similarly offset and the connector lines cross incorrectly.

**Expected:** Each logical F-key should point to the corresponding physical key, e.g. F1 → F1, F2 → F2, etc.

**Actual:** The logical F-key mappings are positionally offset and point to the wrong physical keys.

### Diagnostics report

```markdown

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### `openlogi list` output

```text

```

### Logs

```shell

```

### macOS permissions (if applicable)

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

Start by reproducing the issue from the keyboard configuration/mapping screen on the MX Mechanical Mini for Mac, focusing on the F-key mapping overlay. Trace how logical F-key indices become physical key coordinates; done means F1 points to F1, F2 to F2, and the remaining connector lines no longer show the positional offset.

Written by the indexing model from the issue text.