feat(bar): idle-inhibit (caffeine) toggle — generated bar + summer-day parity (item 13 slice)

Summer-night's whole-swap bar had an idle_inhibitor the generated bar
lacked (reverse parity gap from the 2026-07-04 sweep). The generated
bar now carries it — 󰾪 click → 󰅶, warm tint while active, tooltips
saying what it holds — blocking hypridle's lock/display-off/suspend
for videos and presentations; state deliberately resets with the bar.
summer-day mirrors summer-night's module + CSS, and the keybinds
cheatsheet mentions the bar click (via keybinds.extra).

V1: rendered config has the module with correct glyphs, CSS rules
present, cheatsheet row renders. Inhibit behaviour needs a session →
V3 queued.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

agent/HARDWARE-QUEUE.md

@@ -86,6 +86,10 @@ QA machine), the **T14s** (webcam case).
       `sudo nomarchy-snapshots`, restore a single file (`undochange`)
       and walk a root-config rollback up to (or through) the
       typed-`yes` gate.
+- [ ] **Caffeine toggle (item 13 slice)** — click 󰾪 in the bar → turns
+      󰅶 (warm tint on the generated bar) and hypridle must NOT lock /
+      blank while it's on (wait past the 5-min lock); click again
+      releases. Also present on both summer bars now.
 - [ ] **Screen recording (item 12)** — Tools › Capture: Record region
       (slurp) and Record screen produce a playable .mp4 in
       ~/Videos/Recordings; the red ⏺ REC appears in the bar instantly