diff --git a/apps/web/src/components/ChatView.tsx b/apps/web/src/components/ChatView.tsx
index 84f8b7ee509..352e23c3b1c 100644
--- a/apps/web/src/components/ChatView.tsx
+++ b/apps/web/src/components/ChatView.tsx
@@ -1934,6 +1934,8 @@ function ChatViewContent(props: ChatViewProps) {
         items.push({
           id: `environment-unavailable:${activeEnvironmentUnavailableState.environmentId}`,
           variant: "default",
+          // Live connection status: calm styling, but it must front the stack.
+          urgent: true,
           icon: (
             <span
               className="size-1.5 animate-status-pulse rounded-full bg-foreground"
@@ -1988,6 +1990,9 @@ function ChatViewContent(props: ChatViewProps) {
       items.push({
         id: `server-version:${serverUpdateEnvironmentId}`,
         variant: updateFailed ? "error" : "default",
+        // A running update is live progress the user is waiting on; only the
+        // idle "update available" offer is calm enough to stack behind.
+        urgent: updateInProgress,
         // In-flight and failed states carry their own status dot inside
         // ServerUpdateProgress; only the idle offer needs an icon.
         icon:
@@ -4372,8 +4377,12 @@ function ChatViewContent(props: ChatViewProps) {
     };
   }, [acknowledgeActiveThreadWoke, activeThread?.id, activeThreadWokeVisible]);
   // The stack renders items[0] front-most and tucks the rest behind hover, so
-  // ordering is priority: system banners, then the branch-mismatch notice,
-  // and the informational parked-thread banner last — it must never cover another.
+  // ordering is priority: urgent system banners (error/warning variants plus
+  // calm-styled live states flagged `urgent`, like update progress), then
+  // background liveness — its Stop button is the only stop affordance for
+  // settled turns, so a passive "update available" notice must not cover it —
+  // then calm system banners, the woke and branch-mismatch notices, and the
+  // informational parked-thread banner last — it must never cover another.
   const parkedThreadBannerItem = useMemo<ComposerBannerStackItem | null>(() => {
     if (!activeThreadSnoozed && !activeThreadSettled) {
       return null;
@@ -4423,21 +4432,27 @@ function ChatViewContent(props: ChatViewProps) {
     void handleSwitchCheckoutToThread();
   }, [gitStatusQuery.data?.hasWorkingTreeChanges, handleSwitchCheckoutToThread]);
   const composerBannerItems = useMemo<ComposerBannerStackItem[]>(() => {
+    const isUrgentSystemItem = (item: ComposerBannerStackItem) =>
+      item.urgent === true || item.variant === "error" || item.variant === "warning";
+    const urgentSystemItems = systemComposerBannerItems.filter(isUrgentSystemItem);
+    const calmSystemItems = systemComposerBannerItems.filter((item) => !isUrgentSystemItem(item));
     const backgroundLivenessItems =
       backgroundLivenessBannerItem === null ? [] : [backgroundLivenessBannerItem];
     const wokeThreadItems = wokeThreadBannerItem === null ? [] : [wokeThreadBannerItem];
     const parkedThreadItems = parkedThreadBannerItem === null ? [] : [parkedThreadBannerItem];
     if (!localCheckoutBranchMismatch || !showBranchMismatchBanner || !activeBranchMismatchKey) {
       return [
-        ...systemComposerBannerItems,
+        ...urgentSystemItems,
         ...backgroundLivenessItems,
+        ...calmSystemItems,
         ...wokeThreadItems,
         ...parkedThreadItems,
       ];
     }
     return [
-      ...systemComposerBannerItems,
+      ...urgentSystemItems,
       ...backgroundLivenessItems,
+      ...calmSystemItems,
       ...wokeThreadItems,
       {
         id: `branch-mismatch:${activeBranchMismatchKey}`,
diff --git a/apps/web/src/components/chat/ComposerBannerStack.test.tsx b/apps/web/src/components/chat/ComposerBannerStack.test.tsx
index 1b592168c20..6eed4fb0531 100644
--- a/apps/web/src/components/chat/ComposerBannerStack.test.tsx
+++ b/apps/web/src/components/chat/ComposerBannerStack.test.tsx
@@ -3,9 +3,12 @@ import { describe, expect, it } from "vite-plus/test";
 
 import { ComposerBannerStack, type ComposerBannerStackItem } from "./ComposerBannerStack";
 
-const banner = (id: string): ComposerBannerStackItem => ({
+const banner = (
+  id: string,
+  variant: ComposerBannerStackItem["variant"] = "warning",
+): ComposerBannerStackItem => ({
   id,
-  variant: "warning",
+  variant,
   icon: <span aria-hidden="true">!</span>,
   title: `${id} warning`,
 });
@@ -29,6 +32,19 @@ describe("ComposerBannerStack", () => {
     expect(markup).toContain("group-focus-within/banner-stack:visible");
   });
 
+  it("colors the collapsed stack cap by the hidden banner's variant, not a fixed warning", () => {
+    const neutralBehind = renderToStaticMarkup(
+      <ComposerBannerStack items={[banner("front", "default"), banner("stacked", "default")]} />,
+    );
+    expect(neutralBehind).toContain("border-border");
+    expect(neutralBehind).not.toContain("border-warning/24");
+
+    const warningBehind = renderToStaticMarkup(
+      <ComposerBannerStack items={[banner("front", "default"), banner("stacked", "warning")]} />,
+    );
+    expect(warningBehind).toContain("border-warning/24");
+  });
+
   it("does not render an expandable region for a single banner", () => {
     const markup = renderToStaticMarkup(<ComposerBannerStack items={[banner("front")]} />);
 
diff --git a/apps/web/src/components/chat/ComposerBannerStack.tsx b/apps/web/src/components/chat/ComposerBannerStack.tsx
index 548bd0f4262..41a717d07ce 100644
--- a/apps/web/src/components/chat/ComposerBannerStack.tsx
+++ b/apps/web/src/components/chat/ComposerBannerStack.tsx
@@ -22,9 +22,23 @@ const exitTransitionStyle = {
   transition: `transform ${DISMISS_TRANSITION_MS}ms ease-in, opacity ${DISMISS_TRANSITION_MS}ms ease-in`,
 } satisfies CSSProperties;
 
+// The collapsed cap peeking above the front banner is the only hint that more
+// banners are stacked behind it, so its border must match the severity of the
+// first hidden banner — a neutral banner must not masquerade as a warning.
+const stackCapBorderClass: Record<ComposerBannerStackItem["variant"], string> = {
+  default: "border-border",
+  error: "border-destructive/24",
+  info: "border-info/24",
+  success: "border-success/24",
+  warning: "border-warning/24",
+};
+
 export interface ComposerBannerStackItem {
   readonly id: string;
   readonly variant: "default" | "error" | "info" | "success" | "warning";
+  // Ordering hint for stack assemblers: front this banner even though its
+  // variant is calm (e.g. live update progress). The stack itself ignores it.
+  readonly urgent?: boolean;
   readonly icon: ReactNode;
   readonly title: ReactNode;
   readonly description?: ReactNode;
@@ -67,6 +81,7 @@ export function ComposerBannerStack({ className, items }: ComposerBannerStackPro
   const stackedItems = items.slice(1);
   const hasStack = stackedItems.length > 0;
   const showCollapsedStackCap = hasStack && exitingItemId !== frontItem.id;
+  const firstStackedItem = stackedItems[0];
 
   const requestDismiss = (item: ComposerBannerStackItem) => {
     if (!item.onDismiss || exitingItemId) {
@@ -90,11 +105,12 @@ export function ComposerBannerStack({ className, items }: ComposerBannerStackPro
           hasStack ? "group-hover/banner-stack:z-50 group-focus-within/banner-stack:z-50" : null,
         )}
       >
-        {showCollapsedStackCap ? (
+        {showCollapsedStackCap && firstStackedItem ? (
           <div
             className={cn(
               "pointer-events-none absolute inset-x-0 -top-3 z-0 mx-auto h-3 rounded-t-[22px]",
-              "border border-b-0 border-warning/24 bg-background/96 shadow-[0_6px_18px_rgba(0,0,0,0.06)]",
+              "border border-b-0 bg-background/96 shadow-[0_6px_18px_rgba(0,0,0,0.06)]",
+              stackCapBorderClass[firstStackedItem.variant],
               "transition-opacity duration-150 ease-out",
               "group-hover/banner-stack:opacity-0 group-focus-within/banner-stack:opacity-0",
             )}