test(gsd): add regression tests for autoStartTime persistence (#3585)

Source-code guards verifying autoStartTime is saved in paused-session.json,
restored on both resume paths, and falls back to Date.now() when missing.

src/resources/extensions/gsd/tests/auto-start-time-persistence.test.ts

@@ -0,0 +1,50 @@
+// GSD2 — Verify autoStartTime is persisted in paused-session.json and restored on resume
+// Copyright (c) 2026 Jeremy McSpadden <jeremy@fluxlabs.net>
+
+/**
+ * auto-start-time-persistence.test.ts — Ensures autoStartTime survives
+ * cross-session resume via paused-session.json (#3585).
+ *
+ * Source-code regression guards: verify auto.ts saves and restores
+ * autoStartTime so the elapsed timer doesn't vanish after /exit + resume.
+ */
+
+import test from "node:test";
+import assert from "node:assert/strict";
+import { readFileSync } from "node:fs";
+import { join, dirname } from "node:path";
+import { fileURLToPath } from "node:url";
+
+const __dirname = dirname(fileURLToPath(import.meta.url));
+const AUTO_TS_PATH = join(__dirname, "..", "auto.ts");
+
+const source = readFileSync(AUTO_TS_PATH, "utf-8");
+
+test("pauseAuto persists autoStartTime in paused-session.json (#3585)", () => {
+  assert.ok(
+    source.includes("autoStartTime: s.autoStartTime"),
+    "pausedMeta must include autoStartTime so the timer survives /exit",
+  );
+});
+
+test("cross-session resume restores autoStartTime from paused-session.json (#3585)", () => {
+  const matches = source.match(/s\.autoStartTime\s*=\s*meta\.autoStartTime/g);
+  assert.ok(
+    matches && matches.length >= 2,
+    "both resume paths (custom workflow + milestone) must restore autoStartTime from meta",
+  );
+});
+
+test("resume path falls back to Date.now() when autoStartTime is missing (#3585)", () => {
+  assert.ok(
+    source.includes("meta.autoStartTime || Date.now()"),
+    "restore should fall back to Date.now() for old paused-session files without autoStartTime",
+  );
+});
+
+test("resume path guards against zero autoStartTime (#3585)", () => {
+  assert.ok(
+    source.includes("if (!s.autoStartTime || s.autoStartTime <= 0) s.autoStartTime = Date.now()"),
+    "resume path must set autoStartTime to Date.now() if still zero after restore",
+  );
+});