Background agents → sidebar section (owner): the retired floating dock's successor

The old activity dock (fixed bottom-right, every view) was a cross-session
widget parked inside the session view — the same boundary confusion that
got the plan window moved. The sidebar is the app's cross-session surface,
so the agents section lives at its bottom strip now (user-locked design):

- ALWAYS present: empty means empty — the header ('Background agents',
  matching the Sessions label language) sits alone; nothing hides and
  nothing decorates (the total-cost span only renders when populated).
- Populates and grows when processes run: same blobs (sub-agents +
  extraction runs, one poll, inferred cost, elapsed heartbeat), capped by
  max-h-[40dvh] + internal scroll so a pile never crowds the session list.
- Per-blob END button (unchanged abort contract); the detail popover
  becomes an INLINE expansion — the section scrolls, a floating popover
  would clip at its bounds.
- Sidebar-native skin: border-t separator matching the sidebar's edge,
  session-row hover language, no floating-card chrome.
- Sidebar closed = the learner opted out; no ambient signal for now
  (user decision — invisibility until a clearer observability story).
- Narrow-mode count badge/drawer machinery retired with the dock.

app/layout.tsx: ActivityDock mount removed, ActivityProvider stays (the
sidebar consumes the context). Live-verified: populated rows with inline
detail + session link, abort makes the row vanish, idle renders the
header alone, closed sidebar hides the section with nothing floating.
Gates: typecheck, lint, 423/423 tests.

app/layout.tsx

@@ -3,7 +3,7 @@ import { JetBrains_Mono, Source_Sans_3 } from "next/font/google";
 import "katex/dist/katex.min.css";
 import "./globals.css";
 import { AppShell, SidebarProvider } from "@/components/sidebar";
-import { ActivityDock, ActivityProvider } from "@/components/activity-dock";
+import { ActivityProvider } from "@/components/activity-dock";
 
 // Chrome = JetBrains Mono, teaching prose = Source Sans 3, titles = CMU
 // Serif (the bundled lh-cmu @font-face in globals.css — no CDN).
@@ -20,13 +20,10 @@ export default function RootLayout({ children }: { children: React.ReactNode })
 		<html lang="en" className={`dark ${ui.variable} ${prose.variable}`}>
 			<body className="min-h-dvh antialiased">
 			<SidebarProvider>
-									<ActivityProvider>
-						<AppShell>{children}</AppShell>
-						{/* The reserved bottom-right corner of every view — renders
-					    nothing while no background process runs. */}
-						<ActivityDock />
-					</ActivityProvider>
-							</SidebarProvider>
+				<ActivityProvider>
+					<AppShell>{children}</AppShell>
+				</ActivityProvider>
+			</SidebarProvider>
 		</body>
 		</html>
 	);