fix: import dedup off-switch honesty + brain-owned lifecycle for the background pass

The post-import background deduplication pass (a merge-DELETE writer,
debounced ~5 minutes after import) had four lifecycle defects:

- enableDeduplication: false did not gate the background schedule — an
  import that explicitly opted out could still have entities auto-removed
  minutes later. The flag now gates both the inline and background passes.
- Each import() constructed its own coordinator-owned deduplicator, so the
  debounce never spanned imports (N imports = N delete timers). The brain
  now owns a single lazy instance (getBackgroundDeduplicator).
- close() never cancelled pending dedup; a delete pass could fire against
  a closed brain. close() now cancels it first.
- The 5-minute timer held the process open (exit-hang class); now unref'd.

Four regression tests pin the contract (background-dedup-lifecycle);
import guides document that false disables both passes.

tests/integration/background-dedup-lifecycle.test.ts

@@ -0,0 +1,85 @@
+/**
+ * @module tests/integration/background-dedup-lifecycle
+ * @description The post-import background deduplication pass (a merge-DELETE
+ * writer) obeys the same contract as the inline pass. Laws:
+ * (1) enableDeduplication:false schedules NO background pass — the brain-owned
+ *     deduplicator is never even constructed;
+ * (2) by default the pass IS scheduled, brain-owned, with an unref'd timer
+ *     (a pending pass never holds the process open);
+ * (3) repeated imports debounce into ONE pending batch on ONE instance
+ *     (per-coordinator instances used to arm one timer per import);
+ * (4) close() cancels pending work — no delete pass can fire after close.
+ */
+import { describe, it, expect, beforeEach, afterEach } from 'vitest'
+import { Brainy } from '../../src/brainy.js'
+
+const ROWS = [
+  { name: 'Alice Zephyr', role: 'engineer' },
+  { name: 'Bob Quill', role: 'writer' }
+]
+
+// Keep imports fast and deterministic — dedup scheduling is what's under test.
+const FAST = {
+  enableNeuralExtraction: false,
+  enableRelationshipInference: false,
+  enableConceptExtraction: false
+} as const
+
+// Deterministic stub embedder (hnsw-rebuild.test.ts pattern) — dedup
+// scheduling never inspects vector CONTENT, so skip the WASM model load.
+const stubEmbedding = async (text: string): Promise<number[]> => {
+  const hash = text.split('').reduce((acc, char) => acc + char.charCodeAt(0), 0)
+  const vector = new Array(384).fill(0).map((_, i) => Math.sin(hash + i))
+  return vector
+}
+
+describe('background dedup lifecycle', () => {
+  let brain: Brainy
+
+  beforeEach(async () => {
+    brain = new Brainy({
+      requireSubtype: false,
+      storage: { type: 'memory' as const },
+      embeddingFunction: stubEmbedding
+    })
+    await brain.init()
+  })
+
+  afterEach(async () => {
+    await brain.close()
+  })
+
+  it('enableDeduplication:false schedules no background pass at all', async () => {
+    await brain.import(ROWS, { ...FAST, enableDeduplication: false })
+    expect((brain as any)._backgroundDedup).toBeUndefined()
+  })
+
+  it('default schedules a brain-owned pass with an unref-ed timer', async () => {
+    await brain.import(ROWS, { ...FAST })
+    const dedup = (brain as any)._backgroundDedup
+    expect(dedup).toBeDefined()
+    expect(dedup.pendingImports.size).toBe(1)
+    const timer = dedup.debounceTimer
+    expect(timer).toBeDefined()
+    // Node timers expose hasRef(); an unref'd timer must not hold the process.
+    expect(typeof timer.hasRef).toBe('function')
+    expect(timer.hasRef()).toBe(false)
+  })
+
+  it('imports debounce into one pending batch on one brain-owned instance', async () => {
+    await brain.import(ROWS, { ...FAST })
+    const first = (brain as any)._backgroundDedup
+    await brain.import([{ name: 'Cara Vex', role: 'analyst' }], { ...FAST })
+    expect((brain as any)._backgroundDedup).toBe(first)
+    expect(first.pendingImports.size).toBe(2)
+  })
+
+  it('close() cancels pending background dedup', async () => {
+    await brain.import(ROWS, { ...FAST })
+    const dedup = (brain as any)._backgroundDedup
+    expect(dedup.debounceTimer).toBeDefined()
+    await brain.close()
+    expect(dedup.debounceTimer).toBeUndefined()
+    expect(dedup.pendingImports.size).toBe(0)
+  })
+})