fix(plugins): serverIsLive() falsely reported a server as running

resolveAllDashboardPorts() falls back to [DEFAULT_PORT] when the discovery
file has no live entry — a reasonable guess for the CLI/hook handler, but
wrong for the bootstrap's own liveness check: with no server running at all,
the bootstrap believed one was already up and never called startDashboard(),
confirmed against a real plugin install where the dashboard never started.
plugin-doctor.js's "Server" row had the same bug. Both now read the discovery
file directly and check PID liveness via the new liveServers() (livePids()
reused it instead of duplicating the read).

server/__tests__/plugin-bootstrap.test.js

@@ -31,6 +31,38 @@ after(() => {
   fs.rmSync(TMP_HOME, { recursive: true, force: true });
 });
 
+describe("serverIsLive", () => {
+  const infoPath = path.join(TMP_HOME, ".agent-dashboard.json");
+
+  beforeEach(() => fs.rmSync(infoPath, { force: true }));
+  after(() => fs.rmSync(infoPath, { force: true }));
+
+  it("is false with no discovery file at all", () => {
+    // Regression: server-info's resolveAllDashboardPorts() falls back to
+    // [DEFAULT_PORT] when nothing is live (a reasonable guess for the CLI),
+    // which made the bootstrap wrongly believe a server was already running
+    // and skip starting its own.
+    assert.equal(boot.serverIsLive(), false);
+  });
+
+  it("is false when every recorded pid is dead", () => {
+    fs.writeFileSync(
+      infoPath,
+      JSON.stringify({ servers: [{ port: 4820, pid: 999999, startedAt: "x" }] })
+    );
+    assert.equal(boot.serverIsLive(), false);
+  });
+
+  it("is true when a recorded pid is actually alive", () => {
+    fs.writeFileSync(
+      infoPath,
+      JSON.stringify({ servers: [{ port: 4820, pid: process.pid, startedAt: "x" }] })
+    );
+    assert.equal(boot.serverIsLive(), true);
+    assert.deepEqual(boot.liveServers(), [{ port: 4820, pid: process.pid, startedAt: "x" }]);
+  });
+});
+
 describe("runtime location", () => {
   it("lives under the shared data dir, not the plugin cache", () => {
     assert.equal(boot.runtimeDir(), RT);