## Summary

`omarchy-launch-webapp` silently fails for any default browser that is not on its hardcoded allowlist. When the allowlist misses, it falls back to `chromium.desktop`, and if Chromium is not installed the resolved command is **empty** — so `uwsm-app` is invoked with no binary and reports a misleading error about a nonexistent file path.

This breaks every Omarchy webapp shortcut (`omarchy-launch-webapp` .desktop entries) for affected users.

## Steps to reproduce

1. Set a default web browser whose `.desktop` filename is not on the allowlist (Zen is the common case: `xdg-settings get default-web-browser` -> `zen.desktop`).
2. Do **not** have `chromium` installed.
3. Launch any webapp shortcut that uses `omarchy-launch-webapp`, e.g. `~/.local/share/applications/Google Maps.desktop` or the ones Omarchy generates for third-party web apps.
4. No window opens.

## Actual

```
$ gtk-launch "Google Maps.desktop"
$ journalctl --user -f
uwsm_app-daemon[1263]: received: app -- --app=https://maps.google.com
uwsm_app-daemon[1263]: sent: error 'Error: Path "--app=https:/maps.google.com" does not exist!' 1
```

The error names a "Path" that is really a browser command-line flag, so it gives no hint that the real problem is an empty browser command.

## Expected

Either the webapp window opens, or the failure names the actual cause — e.g. `omarchy-launch-webapp: no Exec found for chromium.desktop; install chromium or set a supported default browser`.

## Root cause

`/usr/share/omarchy/bin/omarchy-launch-webapp`:

```bash
browser=$(xdg-settings get default-web-browser)

case $browser in
google-chrome* | brave* | microsoft-edge* | opera* | vivaldi* | helium*) ;;
*) browser="chromium.desktop" ;;
esac

exec setsid uwsm-app -- $(sed -n 's/^Exec=\([^ ]*\).*/\1/p' {~/.local,~/.nix-profile,/usr}/share/applications/$browser 2>/dev/null | head -1) --app="$1" "${@:2}"
```

Two problems compound:

1. **The allowlist is incomplete.** Zen, Vivaldi forks, Floorp, LibreWolf, Waterfox, Chromium, and any other Chromium/Firefox derivative are all missing, so they are silently rewritten to `chromium.desktop`.
2. **The empty result is not detected.** If the `sed` lookup finds nothing, the command substitution expands to zero arguments and `uwsm-app` receives only `--app=<url>`. `uwsm-app` then treats `--app=...` as a file to open and fails with the "Path does not exist" message above.

## Suggested fix

Prefer the default browser's own `Exec` unconditionally, and use the `chromium.desktop` fallback only when the default browser cannot be resolved — then verify it resolved before exec'ing:

```bash
browser=$(xdg-settings get default-web-browser)

exec_line=$(sed -n 's/^Exec=\([^ ]*\).*/\1/p' {~/.local,~/.nix-profile,/usr}/share/applications/$browser 2>/dev/null | head -1)

if [[ -z $exec_line ]]; then
  browser=chromium.desktop
  exec_line=$(sed -n 's/^Exec=\([^ ]*\).*/\1/p' {~/.local,~/.nix-profile,/usr}/share/applications/$browser 2>/dev/null | head -1)
fi

if [[ -z $exec_line ]]; then
  echo "omarchy-launch-webapp: could not resolve an Exec line for $browser; install it or set a different default browser" >&2
  exit 1
fi

exec setsid uwsm-app -- $exec_line --app="$1" "${@:2}"
```

This removes the need to enumerate browsers at all (any browser whose desktop entry has an `Exec` line just works), keeps Chromium as a fallback for a missing/unset default, and turns the silent failure into an actionable message.

A second, smaller issue: `--app="$1"` relies on the caller quoting the URL, but `Exec=` in a desktop file does not use shell quoting, so authors who write `Exec=omarchy-launch-webapp "https://example.com"` are relying on undefined behaviour. Worth documenting in the webapp docs.

## Workaround

Point the `.desktop` entry at the browser directly, bypassing the helper:

```ini
Exec=/opt/zen-browser-bin/zen-bin --app=https://play.pocketcasts.com/
```

## System

- Omarchy: 4.0.4-1
- OS: Omarchy (Arch), kernel 7.2.5-3-omarchy
- Session: Hyprland (Wayland)
- CPU: AMD Ryzen 5 3400G with Radeon Vega Graphics
- GPU: amdgpu
- Default browser: `zen.desktop` (zen-browser-bin 1.22.3b-1, AUR)
- `chromium`: not installed