Every `omarchy plymouth set ...` (including switcher selections) fails with:

```
omarchy-plymouth-set: refusing to publish: directory /usr/share/plymouth/themes/omarchy (must be root-owned and not group- or world-writable) failed validation
```

The unlock screen stays on default forever. `omarchy plymouth reset` fails identically — there is no self-repair path.

Expected: the set succeeds, or the refusal tells the user how to repair.

## Root cause (verified on my machine)

- The theme dir was created by the pre-4.0 ISO install (`stat` Birth 2025-10-13), owned `uid 1000`, mode `700`. I never chowned it.
- Since 4.0.0 the path is owned by the `omarchy-settings` package, whose `.MTREE` expects root-owned `755` — but pacman does not re-chown pre-existing directories on install/upgrade, so the damage persists invisibly.
- 4.0.x `omarchy-plymouth-set` validates root ownership before publishing, so it refuses on every system carrying this legacy dir.

## Repro

```bash
stat -c '%U %a' /usr/share/plymouth/themes/omarchy   # chrstn 700
omarchy plymouth set by theme tokyo-night            # refuses
```

System: Omarchy 4.0.3-1, Intel i7-7700K, NVIDIA GTX 1070.

## Workaround that fixed it

`sudo chown root:root` + `chmod 755` on the dir, then the set succeeds.

## Suggested fix

A migration repairing that dir (same pattern as `1788662350.sh`, which already repairs other user-owned privileged paths from the pre-4.0 era), or an actionable repair hint in the refusal message.