Trim launcher overhead for terminals and web apps (#13423)

omarchy-launch-webapp asked xdg-settings for the default browser with
BROWSER still set to omarchy-launch-browser, which sends it down a
slower path to the same answer: ~105ms instead of ~30ms on every web app
launch. Unset it, as omarchy-launch-browser already does.

omarchy-cmd-terminal-cwd found the focused terminal's shell with pgrep,
which scans all of /proc on every new terminal. Read the terminal's
child lists from /proc instead, keeping the newest child as before.

Web app wrapper overhead drops from ~111ms to ~34ms, and a new terminal
appears in ~77ms instead of ~90ms.

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

bin/omarchy-cmd-terminal-cwd

@@ -11,7 +11,16 @@ if [[ -S $kitty_socket ]]; then
   cwd=$(kitten @ --to "unix:$kitty_socket" ls --match "state:focused" 2>/dev/null |
     jq -r '.[].tabs[].windows[].cwd // empty')
 else
-  shell_pid=$(pgrep -P "$terminal_pid" | tail -n1)
+  # The newest child, as pgrep -P | tail -n1 found it, read from the kernel's
+  # child lists: pgrep scans all of /proc on every new terminal.
+  shell_pid=""
+  for children_file in /proc/"$terminal_pid"/task/*/children; do
+    [[ -r $children_file ]] || continue
+    read -ra children <"$children_file" || true
+    for child in "${children[@]}"; do
+      (( child > ${shell_pid:-0} )) && shell_pid=$child
+    done
+  done
 
   if [[ -n $shell_pid ]]; then
     cwd=$(readlink -f "/proc/$shell_pid/cwd" 2>/dev/null)

bin/omarchy-launch-webapp

@@ -3,7 +3,9 @@
 # omarchy:summary=Launch a URL as a web app in the default supported browser
 # omarchy:args=<url>
 
-browser=$(xdg-settings get default-web-browser)
+# The session sets BROWSER to omarchy-launch-browser, which sends xdg-settings
+# down a slower path (~100ms against ~30ms) to the same answer.
+browser=$(env -u BROWSER xdg-settings get default-web-browser)
 
 case $browser in
 google-chrome* | brave* | microsoft-edge* | opera* | vivaldi* | helium*) ;;