Make the generate lane's bar preference helper-wide

The maintainer still saw the bottom bar: two tabs were connected to the
helper, the tab that won the roll call hid its bar, and the tab on
screen never did. The hide was also applied only at Go, so the wait
before it showed the bar as well.

The helper now owns the preference. `impeccable live --no-live-bar`
posts `/live-bar` right after the helper is up, so the bar never
appears in any tab; an agent target carrying `hideLiveBar` sets the
same flag before the target goes out. The helper broadcasts
`live_bar` to every connected tab, answers `hideLiveBar` on every
`connected` frame (reloads, later tabs) and on `/status`, and the flag
lives as long as the helper. The overlay just follows: no per-tab
memory, no session scoping, the variant controls still show. The same
preference skips the overlay's "No PRODUCT.md found" connect notice,
which sent the user to init inside a lane that runs without context by
design.

Verified in a real Chromium session with two tabs, screenshots at each
stage: idle (bar in both), after Go (bar gone in both), after reloading
both, after the accept during the bake, after a reload after that.

Written with AI assistance (Claude).

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

skill/scripts/live-browser.js

@@ -7215,26 +7215,18 @@
   // actOnAgentTarget around its handleGo call, read once by handleGo.
   let agentTargetForGo = null;
 
-  // An agent target that asked for the helper's bottom bar to stay out of
-  // the way (`live-generate --no-live-bar`) hides it for the life of this
-  // helper instance in this tab: through the reloads a session causes, the
-  // accept, and the bake that follows, until the helper stops and takes
-  // the whole overlay with it. The variant controls still show. Keyed on the
-  // helper token so the next `impeccable live` starts with the bar again.
-  function liveBarHiddenKey() {
-    return 'impeccable-live:hide-bar:' + TOKEN;
-  }
+  // The helper's word on its global bar. The generate lane asks the helper
+  // to keep it out of the way (`impeccable live --no-live-bar`, or an agent
+  // target carrying hideLiveBar), and the helper tells every connected tab
+  // at once (`live_bar`) and every later connection on `connected`, so the
+  // bar stays hidden in every tab, through reloads, the accept, and the
+  // bake, until the helper stops and takes the overlay with it. The variant
+  // controls still show.
+  let liveBarHiddenByHelper = false;
 
-  function rememberLiveBarHidden() {
-    try { sessionStorage.setItem(liveBarHiddenKey(), '1'); } catch { /* storage may be unavailable */ }
-  }
-
-  function forgetLiveBarHidden() {
-    try { sessionStorage.removeItem(liveBarHiddenKey()); } catch { /* storage may be unavailable */ }
-  }
-
-  function liveBarHiddenForThisHelper() {
-    try { return sessionStorage.getItem(liveBarHiddenKey()) === '1'; } catch { return false; }
+  function applyLiveBarPreference(hidden) {
+    liveBarHiddenByHelper = hidden === true;
+    setLiveBarHidden(liveBarHiddenByHelper);
   }
 
   function setLiveBarHidden(hidden) {
@@ -7486,10 +7478,6 @@
         handleGo();
         agentTargetForGo = null;
         if (state === 'GENERATING' && currentSessionId) {
-          if (msg.hideLiveBar === true) {
-            rememberLiveBarHidden();
-            setLiveBarHidden(true);
-          }
           reply({
             ok: true,
             matchCount: resolved.matchCount,
@@ -7525,8 +7513,11 @@
       let msg; try { msg = JSON.parse(e.data); } catch { return; }
       switch (msg.type) {
         case 'connected':
+          applyLiveBarPreference(msg.hideLiveBar === true);
           hasProjectContext = !!msg.hasProjectContext;
-          if (!hasProjectContext) showToast(`No PRODUCT.md found. Variants will be brand-agnostic. Run ${IMPECCABLE_COMMAND} init to generate one.`, 7000);
+          // The generate lane runs without PRODUCT.md by design and never
+          // sends the user to init, so its quiet chrome skips this notice.
+          if (!hasProjectContext && !liveBarHiddenByHelper) showToast(`No PRODUCT.md found. Variants will be brand-agnostic. Run ${IMPECCABLE_COMMAND} init to generate one.`, 7000);
           console.log('[impeccable] Live mode connected.');
           syncAgentPollingUi(!!msg.agentPolling);
           startAgentStatusPoll();
@@ -7536,6 +7527,9 @@
           syncPageInteractionCursor();
           syncPageChatFocus('sse-connected');
           break;
+        case 'live_bar':
+          applyLiveBarPreference(msg.hidden === true);
+          break;
         case 'agent_polling':
           syncAgentPollingUi(!!msg.connected);
           break;
@@ -11983,9 +11977,9 @@ void main() {
     // Listen for detection results AND ready signal
     window.addEventListener('message', onDetectMessage);
     updateGlobalBarState();
-    // A generate lane asked this helper to keep the bar out of the way; every
-    // reload the session causes rebuilds the bar, so re-apply it here.
-    if (liveBarHiddenForThisHelper()) setLiveBarHidden(true);
+    // The helper may already have said the bar stays hidden (a connect
+    // that raced the bar build, or a reload mid-lane): re-apply it here.
+    if (liveBarHiddenByHelper) setLiveBarHidden(true);
   }
 
   function updateGlobalBarState() {
@@ -12188,7 +12182,7 @@ void main() {
     // not refuse every target the next connection hears.
     busyDeclinedTargets.clear();
     agentTargetsSeen.clear();
-    forgetLiveBarHidden();
+    liveBarHiddenByHelper = false;
     stopAgentStatusPoll();
     hideAgentPollTooltip();
     if (agentPollTooltipEl) {