### System details

omarchy version 4.0.3-1

### What's wrong?

## What happened

Setting a `.desktop`-based default web browser whose `Exec=` line is wrapped
in another command (e.g. `Exec=/usr/bin/env python3 script.py %u`, or a
Flatpak's `Exec=/usr/bin/flatpak run org.example.App %u`) makes every
Omarchy keybinding that opens "the browser" (SUPER+SHIFT+RETURN,
SUPER+SHIFT+B, SUPER+SHIFT+ALT+B, and anything else routed through
`omarchy-launch-browser`) silently do nothing. No error, no notification —
the shortcut just appears dead.

## Why

`omarchy-launch-browser` extracts the executable from the default browser's
`.desktop` entry with:

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

This only captures the first whitespace-separated token after Exec=. For
a normal browser (Exec=firefox %u) that's correct. But when the entry is
wrapped, it captures the wrapper with no arguments:

- Exec=/usr/bin/env python3 .../app.py %u → captures /usr/bin/env
- Exec=/usr/bin/flatpak run org.example.App %u → captures /usr/bin/flatpak

The script then runs that bare command via:

systemd-run --user --quiet --collect --unit="omarchy-browser-$(date +%s%N)" \
  --property=StandardOutput=null --property=StandardError=null \
  uwsm-app -- "$browser_exec" "${@/--private/$private_flag}"

env with no arguments just prints the environment and exits; flatpak
with no subcommand prints usage. Neither opens a window, and because
stdout/stderr are redirected to /dev/null, there's no visible sign of
failure anywhere.

Steps to reproduce

1. Install any app registered as a web browser (x-scheme-handler/https +
   Categories=...WebBrowser...) whose .desktop Exec= line starts with a
   wrapper, e.g.:
Exec=/usr/bin/env python3 /path/to/script.py %u
2. xdg-settings set default-web-browser <that-app>.desktop
3. Press SUPER+SHIFT+RETURN (or run omarchy-launch-browser directly).
4. Nothing happens. journalctl --user -u 'omarchy-browser-*' shows the
   transient unit ran and exited 0 — it just ran env/flatpak with no args.

Minimal repro without installing anything, once a wrapped app is the
default:
env -u BROWSER xdg-settings get default-web-browser
sed -n 's/^Exec=\([^ ]*\).*/\1/p' ~/.local/share/applications/<id>.desktop
# prints "/usr/bin/env" (or "/usr/bin/flatpak") instead of the real app

Expected

omarchy-launch-browser should run the full Exec= command (minus the
%u/%U field code, with the URL substituted or appended), not just its
first token — the same way gtk-launch <desktop-id> <url> or
gio launch <file>.desktop <url> would handle it correctly, since both
resolve the whole Exec line rather than re-parsing it by hand.

System

- Omarchy version: 4.0.3-1
- Script: /usr/share/omarchy/bin/omarchy-launch-browser
- Triggered via the default keybindings (SUPER+SHIFT+RETURN / SUPER+SHIFT+B
  / SUPER+SHIFT+ALT+B), which call omarchy-launch-browser through the
  { omarchy = "browser" } binding helper.

Happy to test a fix — this reproduces reliably with any env- or
flatpak-wrapped default browser entry.

## Related

Same underlying bug as #10988 (`omarchy-launch-webapp`), just in the sibling
script `bin/omarchy-launch-browser` — both use the same
`sed -n 's/^Exec=\([^ ]*\).*/\1/p'` pattern to extract the browser binary from
a `.desktop` Exec= line, and both break the same way on any wrapped Exec
(`env ...`, `flatpak run ...`). Might be worth fixing both call sites with the
same approach.