Drop bin/omarchy-menu; sweep JSONC actions to bare commands

The shell now owns the menu — both data and dispatch. The 821-line bash
bin was carrying the open path (cold spawn + jq pipeline + tempfile dance
+ IPC + poll) and a grab-bag of helpers that only existed inside it. Both
go away in this commit.

New bins for the few composite helpers that were genuinely worth keeping:

  - omarchy-install-app NAME PKG
  - omarchy-install-and-launch NAME PKG DESKTOP_ID
  - omarchy-install-font LABEL PKG FAMILY
  - omarchy-launch-config-editor PATH
  - omarchy-reminder-set-interactive
  - omarchy-capture-screenrecording-with-webcam

Sweep through default/omarchy/omarchy-menu.jsonc rewrites:

  - present_terminal X   -> omarchy-launch-floating-terminal-with-presentation X
  - install_terminal X   -> omarchy-launch-floating-terminal-with-presentation 'omarchy-install-terminal X'
  - install / install_and_launch / install_font / open_in_editor -> new bins above
  - terminal X           -> xdg-terminal-exec --app-id=org.omarchy.terminal X
  - default_browser_is X -> [[ "$(omarchy-default-browser)" == "X" ]]
  - default_terminal_is X / default_editor_is X / haptic_touchpad_is X same shape
  - $(hypr_config_file X) -> ~/.config/hypr/X.lua
  - show_custom_reminder_input -> omarchy-reminder-set-interactive
  - screenrecord_with_webcam   -> omarchy-capture-screenrecording-with-webcam
  - stop_active_screenrecording -> omarchy-capture-screenrecording --stop-recording

Hyprland bindings switch from `omarchy-menu X` to
`omarchy-shell-ipc menu summon X` (the keybind hot path now skips bash
entirely). The Bar.qml omarchy widget and the battery right-click do the
same. ALT+PRINT becomes a one-liner: stop the recording if one is going,
otherwise summon the screenrecord submenu.

Measured: keybind-to-visible is ~30ms (was ~235ms). The shell's plugin
keepLoaded:true stops being theoretical \u2014 the menu data lives in memory
across opens, and the only work between keypress and paint is the IPC
roundtrip and the layer-shell window mount.

bin/omarchy-capture-screenrecording-with-webcam

@@ -0,0 +1,36 @@
+#!/bin/bash
+
+# omarchy:summary=Pick a webcam and start a screen recording with it
+# omarchy:examples=omarchy capture screenrecording-with-webcam
+
+set -o pipefail
+
+webcam_list() {
+  v4l2-ctl --list-devices 2>/dev/null | while IFS= read -r line; do
+    if [[ $line != $'\t'* && -n $line ]]; then
+      local name="$line"
+      local device
+      IFS= read -r device || break
+      device=$(tr -d '\t' <<<"$device" | head -1)
+      [[ -n $device ]] && echo "$device  $name"
+    fi
+  done
+}
+
+devices=$(webcam_list)
+if [[ -z $devices ]]; then
+  omarchy-notification-send "No webcam devices found" -u critical -t 3000
+  exit 1
+fi
+
+count=$(grep -c . <<<"$devices")
+if (( count == 1 )); then
+  device="${devices%%[[:space:]]*}"
+else
+  selection=$(omarchy-menu-select "Select Webcam" "$devices") || exit 1
+  device="${selection%%[[:space:]]*}"
+fi
+
+exec omarchy-capture-screenrecording \
+  --with-desktop-audio --with-microphone-audio \
+  --with-webcam --webcam-device="$device"