Ensure that $BROWSER runs omarchy-launch-browser and doesn't hand ownership to parent process

This prevents gh auth login from working without an existing open
browser

bin/omarchy-launch-browser

@@ -6,7 +6,7 @@
 default_browser=$(xdg-settings get default-web-browser)
 browser_exec=$(sed -n 's/^Exec=\([^ ]*\).*/\1/p' {~/.local,~/.nix-profile,/usr}/share/applications/$default_browser 2>/dev/null | head -1)
 
-if $browser_exec --help | grep -q MOZ_LOG; then
+if $browser_exec --help 2>/dev/null | grep -q MOZ_LOG; then
   private_flag="--private-window"
 elif [[ $browser_exec =~ edge ]]; then
   private_flag="--inprivate"
@@ -14,4 +14,6 @@ else
   private_flag="--incognito"
 fi
 
-exec setsid uwsm-app -- "$browser_exec" "${@/--private/$private_flag}"
+systemd-run --user --quiet --collect --unit="omarchy-browser-$(date +%s%N)" \
+  --property=StandardOutput=null --property=StandardError=null \
+  uwsm-app -- "$browser_exec" "${@/--private/$private_flag}"