### Summary

`omarchy-provision-user` points `DESKTOP`, `TEMPLATES` and `PUBLICSHARE` at `$HOME` and removes the
folders:

```bash
# /usr/bin/omarchy-provision-user  (omarchy 4.0.2-1, lines ~98-101)
xdg-user-dirs-update --set TEMPLATES "$HOME"
xdg-user-dirs-update --set PUBLICSHARE "$HOME"
xdg-user-dirs-update --set DESKTOP "$HOME"
rmdir ~/Templates ~/Public ~/Desktop 2>/dev/null || true
```

The intent is clear and I agree with it — Hyprland has no desktop metaphor, so three permanently empty
folders are noise. Pointing an XDG dir at the home directory is also the freedesktop-documented way to
say "this directory doesn't exist here", so this isn't a hack.

**The problem is that apps don't interpret it that way.** Nothing reads `XDG_DESKTOP_DIR=$HOME` as
"there is no desktop, skip it". They read it as "the desktop is `~`" and write there. So the setting
that exists to keep `$HOME` tidy is the thing that untidies it.

### Impact

On one machine, after about a day of ordinary use, `~` had collected:

```
steam.desktop                                     # byte-identical to /usr/share/applications/steam.desktop
chrome-<id>-Default.desktop                       # Chrome PWA shortcut
chrome-<id>-Default.desktop                       # Chrome PWA shortcut
chrome-<id>-Default.desktop                       # Chrome PWA shortcut
```

Two things make this worse than ordinary clutter:

1. **The files are inert.** Walker and the app menu read `~/.local/share/applications/`, where correct
   copies already exist. The `~` copies are never used by anything.
2. **They are stale duplicates.** The Chrome PWA copies in `~` lacked the `%U` argument and the
   `MimeType=` line that the `~/.local/share/applications/` versions carry, so they were also *worse*
   copies — e.g. missing `x-scheme-handler/mailto` registration.

Users are unlikely to connect loose `.desktop` files in `$HOME` to an XDG setting, so they accumulate
indefinitely.

### Reproduce

On a stock Omarchy install:

1. `omarchy-install-steam` (or install Steam by any means) and let it create a desktop shortcut, and/or
2. In Chrome, open any site → **Cast, save and share → Install page as app**
3. `ls ~/*.desktop`

Expected: nothing in `$HOME`. Actual: one `.desktop` file per shortcut.

### Suggested fix

Keep the intent, drop the side effect — give `DESKTOP` a real but out-of-the-way target rather than
`$HOME`:

```bash
xdg-user-dirs-update --set DESKTOP "$HOME/.local/share/desktop"
```

No visible folder in `$HOME`, and anything that insists on writing a desktop shortcut lands somewhere
ignorable. `TEMPLATES` and `PUBLICSHARE` are rarely written to by anything, so they matter less — but
the same reasoning applies.

An alternative, if a hidden path feels wrong, is to leave the folders in place and accept three empty
directories; that at least confines the writes.

### Environment

- omarchy `4.0.2-1`
- `xdg-user-dirs 0.20-1`
- `/etc/xdg/user-dirs.defaults` ships the standard layout (`DESKTOP=Desktop`, `TEMPLATES=Templates`,
  `PUBLICSHARE=Public`); the `$HOME` values come from `omarchy-provision-user`, not the system default.

### Related

- #1331 — proposal that Omarchy avoid creating files in the user's home directory (same concern, other direction)