feat(web): redesign Overview as the homepage with a living graph backdrop

Overview replaces Tasks as the default route: a centered new-task entry
with live fleet metrics, a scrollable/filterable task table, and an
ambient canvas rendering of the real entity graph (autonomous camera
drift + mouse parallax) behind it. Tasks sidebar entry is removed;
its status-bucketing logic moves to lib/tasks.ts for reuse.

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

web/src/lib/tasks.ts

@@ -0,0 +1,53 @@
+// Shared task-status helpers. Used by the Overview homepage (and previously the
+// standalone Tasks board) to map a session's lifecycle onto a small set of
+// display buckets, styles, and filters.
+import type { Session } from '$lib/api'
+
+export type Bucket = 'running' | 'input' | 'done' | 'failed'
+
+export function bucket(s: Session): Bucket {
+  switch (s.status) {
+    case 'awaiting_input':
+      return 'input'
+    case 'done':
+      return s.outcome === 'failure' ? 'failed' : 'done'
+    case 'failed':
+      return 'failed'
+    default:
+      return 'running' // active | planning | executing | undefined
+  }
+}
+
+export interface StatusStyle {
+  label: string
+  dot: string
+  pulse: boolean
+}
+
+export function statusStyle(s: Session): StatusStyle {
+  switch (bucket(s)) {
+    case 'input':
+      return { label: 'Needs input', dot: 'bg-warning', pulse: true }
+    case 'done':
+      return { label: s.outcome === 'partial' ? 'Done · partial' : 'Done', dot: 'bg-success', pulse: false }
+    case 'failed':
+      return { label: 'Failed', dot: 'bg-destructive', pulse: false }
+    default:
+      return { label: 'Running', dot: 'bg-primary', pulse: true }
+  }
+}
+
+export const FILTERS: { id: 'all' | Bucket; label: string }[] = [
+  { id: 'all', label: 'All' },
+  { id: 'running', label: 'Running' },
+  { id: 'input', label: 'Needs input' },
+  { id: 'done', label: 'Done' },
+  { id: 'failed', label: 'Failed' }
+]
+
+// Task events that should trigger a session-board refetch.
+export const TASK_EVENTS = new Set(['task.status', 'goal.set', 'question.raised', 'question.answered'])
+
+export function heading(s: Session): string {
+  return s.goal || s.title || 'Untitled task'
+}