feat(settings): codeman doctor in Settings -> System -> Diagnostics

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

test/doctor-cli-json.test.ts

@@ -0,0 +1,36 @@
+// @vitest-environment node
+// The contract GET /api/doctor's default runner relies on: the same entry script, given
+// `doctor --json`, prints a parseable DependencyReportJson on stdout, even when it exits
+// non-zero because something required is missing.
+
+import { execFile } from 'node:child_process';
+import { join } from 'node:path';
+import { describe, expect, it } from 'vitest';
+
+const ROOT = join(import.meta.dirname, '..');
+
+describe('codeman doctor --json', () => {
+  it('prints a report that includes Node and a summary, whatever the exit code', async () => {
+    const stdout = await new Promise<string>((resolve, reject) => {
+      execFile(
+        process.execPath,
+        [
+          join(ROOT, 'node_modules/tsx/dist/cli.mjs'),
+          join(ROOT, 'src/index.ts'),
+          'doctor',
+          '--json',
+          '--category',
+          'core',
+        ],
+        { timeout: 60_000, cwd: ROOT },
+        (err, out) => (out ? resolve(out) : reject(err ?? new Error('no output')))
+      );
+    });
+    const report = JSON.parse(stdout);
+    expect(report.platform.environment).toMatch(/linux|darwin|win32|wsl/);
+    expect(report.summary).toEqual(expect.objectContaining({ ok: expect.any(Number), exitCode: expect.any(Number) }));
+    const node = report.tools.find((t: { id: string }) => t.id === 'node');
+    expect(node?.status).toBe('ok');
+    expect(report.tools.every((t: { category: string }) => t.category === 'core')).toBe(true);
+  }, 90_000);
+});