## Environment
- Omarchy version: 4.0.0-1
- Hardware: Minisforum AI X1 Pro (AMD Ryzen AI 9 HX 470)
- Fingerprint reader: USB `2541:fa03` — "Realtek USB2.0 Finger Print Bridge"

## Symptom
`omarchy setup security fingerprint` aborts immediately:

```
Setting up fingerprint scanner for authentication.

No fingerprint sensor detected.
```

## Root cause
The detection script `/usr/share/omarchy/bin/omarchy-hw-fingerprint` misses this reader for two reasons:

1. Vendor `2541` is not in `fingerprint_vendors` (`27c6 138a 06cb 08ff 1c7a 147e`).
2. The reader's product string is **"Finger Print"** (two words), but the product match only catches the single word `*fingerprint*`:

```bash
[[ $product == *fingerprint* || $product == *biometric* || ... ]] && exit 0
```

Note: `2541:fa03` is a **supported device** in libfprint (listed as "Realtek MOC Fingerprint Sensor" on https://fprint.freedesktop.org/supported-devices.html), and the device's USB interface has no kernel driver bound, so libfprint/fprintd can claim it directly. The only blocker is Omarchy's detection gate.

## Fix (verified working)
Add `2541` (and `3274`, the other Realtek MOC ID) to the vendor list, and broaden the product match to also catch "Finger Print":

```diff
- fingerprint_vendors=" 27c6 138a 06cb 08ff 1c7a 147e "
+ fingerprint_vendors=" 27c6 138a 06cb 08ff 27c6 08ff 1c7a 147e 2541 3274 "
```

(actual corrected line)
```diff
- fingerprint_vendors=" 27c6 138a 06cb 08ff 1c7a 147e "
+ fingerprint_vendors=" 27c6 138a 06cb 08ff 1c7a 147e 2541 3274 "
```

```diff
-     [[ $product == *fingerprint* || $product == *biometric* || $product == *elan:arm-m4* || $product == "fpc "* ]] && exit 0
+     [[ $product == *fingerprint* || $product == *finger*print* || $product == *biometric* || $product == *elan:arm-m4* || $product == "fpc "* ]] && exit 0
```

After this change, `omarchy setup security fingerprint` detects the reader, `fprintd-enroll` + `fprintd-verify` succeed, and sudo/polkit/lock-screen PAM are configured correctly.

## Note
The patched file lives in the package-managed `/usr/share/omarchy/` and is reverted on the next `omarchy update`, so a permanent fix in the package is needed.