### System details

Omarchy 4.0.0-1 · AMD Ryzen 5 7600X · NVIDIA RTX 3070 (+ AMD Raphael iGPU)

### What's wrong?

### Description

If the user backgrounds directory `~/.config/omarchy/backgrounds/<theme>/` is a symlink (e.g. into a stow/chezmoi-managed dotfiles repo), `omarchy theme bg next` always selects the alphabetically first image and never advances. The same index lookup in `omarchy-theme-set` (`choose_theme_background`) has the identical problem.

Root cause is a path-canonicalisation mismatch between two scripts:

- `bin/omarchy-theme-bg-set:12` stores the current background as `realpath "$1"`, i.e. with the symlink **resolved** (`/home/u/dotfiles/.../foo.jpg`).
- `bin/omarchy-theme-bg-next` builds the candidate list with `find -L "$HOME/.config/omarchy/backgrounds/$THEME_NAME/"`, which yields **unresolved** paths (`/home/u/.config/omarchy/backgrounds/<theme>/foo.jpg`), then does a plain string compare against `readlink` of the state symlink.

The two strings never match, so `INDEX` stays `-1` and the script falls through to `BACKGROUNDS[0]` on every invocation. The first call "works"; every call after that is a no-op.

The background switcher is unaffected because it calls `bg-set` with an explicit file. Stock theme backgrounds are unaffected because `current/theme/backgrounds/` is a real copied directory.

### Steps to reproduce

Isolated, without touching the live setup (stubs `omarchy-shell` so the wallpaper isn't actually changed):

```bash
S=$(mktemp -d)
mkdir -p "$S/home/.local/state/omarchy/current/theme/backgrounds" \
         "$S/home/.config/omarchy/backgrounds" "$S/real-walls" "$S/stubs"
echo t > "$S/home/.local/state/omarchy/current/theme.name"
for f in a b c; do printf x > "$S/real-walls/$f.jpg"; done
printf '#!/bin/sh\nexit 0\n' > "$S/stubs/omarchy-shell"
cp "$S/stubs/omarchy-shell" "$S/stubs/omarchy-notification-send"; chmod +x "$S/stubs"/*

ln -s "$S/real-walls" "$S/home/.config/omarchy/backgrounds/t"
for i in 1 2 3 4; do
  HOME="$S/home" PATH="$S/stubs:$PATH" omarchy-theme-bg-next
  readlink "$S/home/.local/state/omarchy/current/background"
done
```

Or on a real install: `ln -s ~/Pictures/walls ~/.config/omarchy/backgrounds/catppuccin`, run `omarchy theme bg next` a few times, watch `omarchy theme bg current`.

**Expected:** cycles `a.jpg → b.jpg → c.jpg → a.jpg`, as it does when the directory is real (verified with `cp -r` in place of `ln -s`).

**Actual:** `a.jpg` four times.

### Suggested fix

Compare canonical paths on both sides, in `bg-next` and in `choose_theme_background`:

```bash
CURRENT_BACKGROUND=$(readlink -f "$CURRENT_BACKGROUND_LINK")
...
if [[ $(realpath "${BACKGROUNDS[$i]}") == "$CURRENT_BACKGROUND" ]]; then
```

Alternatively drop `realpath` from `bg-set` — but resolving on the comparison side is more robust (also covers `bg set` with a relative path).

Related but distinct: #7668 (`choose_theme_background` fails the same lookup on theme switch, for a different reason). Both would benefit from a canonical-path comparison.