fix(test): decide base-path rejection from the server's own startup line (#93)

The old gate raced child exit against a fixed 800 ms timer. Under full-suite
CPU contention the child was still importing modules, so it was killed and
the timeout was asserted as acceptance: 2/2 full-suite runs on main failed
with '"timmy-staging" was accepted' while the file alone passed 3/3 and the
server rejected the value directly.

Acceptance is now decided by the child printing 'Timmy is listening on
http://'; a child that neither exits nor listens inside 20 s is reported as
indeterminate. Rejection assertions (non-zero exit, TIMMY_BASE_PATH in
stderr) still run.

Mutation check: with the leading-slash validation disabled the repaired
test fails in 398 ms with the acceptance message.

tests/staging-health.test.js

@@ -125,6 +125,30 @@ test('agent cookie is constrained to the normalized base path', async t => {
   assert.match(response.headers.get('set-cookie'), /; Path=\/timmy-staging\//);
 });
 
+// The child's own startup line is the only trustworthy evidence that a base path was accepted.
+// A fixed timer cannot tell "still importing modules" from "server is up": on a loaded host the
+// old 800 ms race killed a correctly-rejecting child and reported it as accepted.
+function startupOutcome(child, deadlineMs = 20_000) {
+  return new Promise(resolve => {
+    let stdout = '';
+    let stderr = '';
+    let settled = false;
+    const finish = outcome => {
+      if (settled) return;
+      settled = true;
+      clearTimeout(timer);
+      resolve({ ...outcome, stdout, stderr });
+    };
+    const timer = setTimeout(() => finish({ timedOut: true }), deadlineMs);
+    child.stdout.on('data', chunk => {
+      stdout += chunk;
+      if (/^Timmy is listening on http:\/\//m.test(stdout)) finish({ listening: true });
+    });
+    child.stderr.on('data', chunk => { stderr += chunk; });
+    child.once('exit', code => finish({ code }));
+  });
+}
+
 test('malformed and escaping base paths are rejected at startup', async () => {
   const invalid = [
     'timmy-staging',
@@ -152,16 +176,17 @@ test('malformed and escaping base paths are rejected at startup', async () => {
     const child = spawn(process.execPath, ['server.mjs'], {
       cwd: root,
       env: { ...process.env, PORT: '0', TIMMY_BASE_PATH: value },
-      stdio: ['ignore', 'ignore', 'pipe'],
+      stdio: ['ignore', 'pipe', 'pipe'],
     });
-    let stderr = '';
-    child.stderr.on('data', chunk => { stderr += chunk; });
-    const exitCode = await Promise.race([
-      new Promise(resolve => child.once('exit', resolve)),
-      new Promise(resolve => setTimeout(() => { child.kill('SIGTERM'); resolve('timeout'); }, 800)),
-    ]);
-    assert.notEqual(exitCode, 'timeout', `${JSON.stringify(value)} was accepted`);
-    assert.notEqual(exitCode, 0, `${JSON.stringify(value)} exited successfully`);
-    assert.match(stderr, /TIMMY_BASE_PATH/);
+    const outcome = await startupOutcome(child);
+    if (outcome.listening) {
+      const closed = new Promise(resolve => child.once('close', resolve));
+      child.kill('SIGKILL');
+      await closed;
+    }
+    assert.equal(outcome.listening, undefined, `${JSON.stringify(value)} was accepted: the server announced it was listening`);
+    assert.notEqual(outcome.timedOut, true, `${JSON.stringify(value)} neither exited nor announced listening within the startup deadline`);
+    assert.notEqual(outcome.code, 0, `${JSON.stringify(value)} exited successfully`);
+    assert.match(outcome.stderr, /TIMMY_BASE_PATH/);
   }
 });