Problem

Fixes #1471 (root cause). Should also resolve the symptom issues that stem from the same module-singleton-null-mid-cycle defect: #1404, #1413, #1491, #1619.

A PostgresEngine connecting via the module-singleton path (no poolSize) is tagged _connectionStyle = 'module' whether it CREATED the shared db.ts sql singleton (the owner - the CLI cycle engine) or merely found it already connected (a borrower - the probe engine in resolveLintContentSanity, doctor, future probes). The old disconnect() called db.disconnect() for BOTH, so a short-lived borrower's finally-block teardown nulled the singleton the owner cycle engine was still using. Every later phase then threw No database connection: connect() has not been called, and runCycle's finally stranded a row in gbrain_cycle_locks.

_connectionStyle alone can't separate owner from borrower - both are 'module'. This implements the ownership-flag fix proposed in #1471.

Fix

• db.ts: add isConnected() so an engine can tell, at connect() time, whether the singleton already exists.
• postgres-engine.ts: add _ownsModuleSingleton. connect() samples ownership before delegating to db.connect(); disconnect() calls db.disconnect() only when this engine owns the singleton. A borrower clears its own marker without touching the shared connection.

Scope:

• Instance-pool engines (poolSize set) are unaffected - they never take the module branch.
• reconnect() stays correct: an owner's disconnect+reconnect re-acquires ownership (the singleton is null right after its own db.disconnect()), and a borrower re-borrows the owner's (possibly refreshed) singleton.

Tests

• New test/postgres-engine-singleton-ownership.test.ts: source-level guardrails (DB-free, matching the existing postgres-engine.test.ts convention, since runtime-mocking postgres.js's tagged-template interface is painful under bun ESM). Asserts db.isConnected() is sampled before db.connect(), and that the only db.disconnect() in disconnect() is guarded by _ownsModuleSingleton.
• bun run typecheck: clean.
• Regression (59 tests green): postgres-engine, db-disconnect-audit, connection-manager.serial, autopilot-reconnect-classifier, worker-shutdown-disconnect.

The live gbrain dream cycle is the e2e exercise of this path; the ownership logic above is what keeps the owner's singleton alive across a borrower probe's teardown.