feat: add 5 PM features — custom statuses, Gantt, quick-add, automations, notifications

- Custom workflow statuses: per-project configurable status definitions
  replacing the fixed task_status enum. Each project defines its own
  workflow with drag-to-reorder, color coding, and category mapping.
- Gantt/timeline view: full project roadmap with task bars, dependency
  arrows, milestone diamonds, zoom levels (day/week/month), and drag
  to reschedule.
- Natural-language quick-add: NLP parser extracts dates, priorities,
  projects, labels, and recurrence from free text. Floating bar with
  'n' shortcut and live parsed preview.
- Automation rules: no-code trigger-action system per project. Triggers
  on status change, task creation, due date approaching. Actions set
  status/priority, add labels, create notifications.
- Notification center: in-app bell icon with unread badge, slide-out
  panel, real-time SSE updates, mark read/all read. Replaces raw
  activity feed dropdown.

Schema: adds status_definitions, automation_rules, notifications tables.
Migrations: 0007, 0008, 0009. 41 NLP parser tests pass.

apps/api/src/lib/notify.ts

@@ -0,0 +1,65 @@
+import { db, sql, notifications, domains } from "@project-e/db";
+import { eq } from "drizzle-orm";
+
+export type NotificationType =
+  | "mention"
+  | "status_change"
+  | "due_soon"
+  | "automation"
+  | "assignment";
+
+export interface CreateNotificationParams {
+  userId: string;
+  workspaceId?: string | null;
+  type: NotificationType | string;
+  title: string;
+  body?: string | null;
+  entityType?: string | null;
+  entityId?: string | null;
+}
+
+/**
+ * Insert an in-app notification and fan it out over the realtime SSE stream so
+ * open clients refresh their bell count and list without polling. The event
+ * mirrors the pg_notify shape used by recordActivity: `{ type, action, id,
+ * workspace_id }` with `type: "notification"`.
+ */
+export async function createNotification(params: CreateNotificationParams): Promise<typeof notifications.$inferSelect> {
+  const { userId, workspaceId, type, title, body, entityType, entityId } = params;
+
+  const [notification] = await db.insert(notifications).values({
+    userId,
+    workspaceId: workspaceId ?? null,
+    type,
+    title,
+    body: body ?? null,
+    entityType: entityType ?? null,
+    entityId: entityId ?? null,
+  }).returning();
+
+  if (workspaceId) {
+    const payload = JSON.stringify({ type: "notification", action: "created", id: notification.id, workspace_id: workspaceId });
+    await sql`SELECT pg_notify('project_e_events', ${payload}::text)`;
+  }
+
+  return notification;
+}
+
+/**
+ * MVP convenience for the single-user app: resolve the workspace owner and send
+ * them the notification. Returns null when the workspace has no owner, so
+ * callers can rely on this never throwing for missing ownership.
+ */
+export async function notifyWorkspaceOwner(params: Omit<CreateNotificationParams, "userId">): Promise<typeof notifications.$inferSelect | null> {
+  const { workspaceId, ...rest } = params;
+  if (!workspaceId) return null;
+
+  const [domain] = await db
+    .select({ ownerId: domains.ownerId })
+    .from(domains)
+    .where(eq(domains.id, workspaceId))
+    .limit(1);
+
+  if (!domain?.ownerId) return null;
+  return createNotification({ ...rest, workspaceId, userId: domain.ownerId });
+}