sway: extract start-swayidle.sh as single source of truth (fix caffeine)

caffeine.sh click was silently breaking idle lock. Two bugs that
compounded:

1. caffeine.sh inlined its own swayidle command (with swaylock -f -i
   , not lock-fancy.sh), drifted out of sync with sway/config
   which used lock-fancy.sh. Toggle off would restart swayidle with a
   different lock command than the rest of the session.

2. WAYLAND_DISPLAY isn't set in waybar's on-click context. When
   caffeine.sh called 'swaymsg output * power off' (part of the
   restart command) and later called swaylock / grim (via lock-fancy),
   those failed silently. swayidle itself can run without
   WAYLAND_DISPLAY but it can't actually monitor input/output, so it
   exits immediately. Result: user clicks caffeine off, flag clears,
   icon goes back to 'inactive', but auto-lock is silently dead.
   The user thinks they turned caffeine off. They didn't. They're
   just unprotected.

Fix:
- new start-swayidle.sh holds the canonical swayidle command
- sway/config: exec $HOME/.config/sway/start-swayidle.sh
- caffeine.sh: killall swayidle; start-swayidle.sh &
- start-swayidle.sh probes /proc/*/environ for a Wayland client's
  env (mako always has it) and exports WAYLAND_DISPLAY /
  DBUS_SESSION_BUS_ADDRESS / XDG_RUNTIME_DIR / DISPLAY if missing
  before exec'ing swayidle

Single source of truth + env restoration = click works on every box
that has the same Wayland-capable process tree (mako, swaybar, etc.),
no matter who/what is calling the script.

Verified on tadbit: pre-fix toggle off killed swayidle permanently.
Post-fix: toggle off restarts swayidle successfully, env inherited
from mako's /proc/PID/environ.

dot_config/sway/config

@@ -55,11 +55,10 @@ exec wlsunset -l 39.96 -L -82.99
 exec sworkstyle
 
 # === idle / lock ===
-exec swayidle -w \
-    timeout 300 '$HOME/.config/sway/lock-fancy.sh' \
-    timeout 600 'swaymsg "output * power off"' \
-    resume 'swaymsg "output * power on"' \
-    before-sleep '$HOME/.config/sway/lock-fancy.sh'
+# Single source of truth: start-swayidle.sh is also called by caffeine.sh
+# to restart swayidle after toggling off the inhibit. Don't inline the
+# swayidle command here — keep the two in sync via the wrapper.
+exec $HOME/.config/sway/start-swayidle.sh
 
 # === keybinds ===
 bindsym $mod+Return exec $term