[Bug]: DPI setting resets on windows reboot, MX Master 3S

### 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

0.6.19

### Operating system

Windows

### OS version & architecture

win 11

### Device model

MX Master 3S

### How is the device connected?

Bluetooth (direct, no receiver)

### Affected area(s)

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

### What happened?

- DPI reset on reboot: There is a closed issue on Mac, but I still couldn't get DPI to persist over reboot.
- DPI cycling through the presets also doesn't work.

### Steps to reproduce

Restart the PC; the DPI resets to default.

Tried to rebind the cycling DPI to other buttons; it also doesn't work.

### Diagnostics report

```markdown
### OpenLogi Diagnostics

**App**
- OpenLogi (GUI): v0.6.19 (release)
- Agent: v0.6.19 (connected)
- IPC protocol: GUI 8 / agent 8
- Inventory: ready
- OS: Windows (x86_64)
- Locale: en-US (UI: follow system)
- Accessibility: granted · Input hook: installed
- Launch at login: yes · Menu bar: yes · Update check: on
- Running from: source build (dev)
- Config: schema 3 · 1 configured device(s) · thumbwheel 14

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

**Devices (1)**
- MX Master 3S — mouse (codename: )
- Connection: Bluetooth (direct) · Online: yes · Battery: 50% (discharging, good)
- Capabilities: buttons=yes, pointer=yes, lighting=no
- DPI: 2000 dpi (range 200–8000, 157 steps)
- Model: direct:046d:b034:serial:2410ap078fq8 (model-ids: b034/0000/0000, ext-model: 00)
- Transports: BTLE
- Render: mx_master_3s · direct
```

### `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).

Start by reproducing the DPI reset after a Windows reboot and the failed preset-cycling binding with the MX Master 3S over direct Bluetooth. Trace the GUI-to-agent DPI control and configuration flow, then verify that the selected DPI persists across reboot and that cycling works without Logi Options+ running.

Written by the indexing model from the issue text.