feat(analytics): instance census, full capture, richer error context (#511)

Add a once-per-boot instance_started event (arch, os, deploy_mode,
gpu_present) so the fleet architecture mix is measurable. It reuses the
existing per-instance instance_id and is exempt from the volume sample
rate, since a census that fires once per boot must not be thinned.

Restore useful capture depth now that the sponsored plan removes the
quota pressure behind the earlier hardening:

- PostHog sample rate 0.1 to 1.0 (full analytics when enabled); the
  property allowlist still blocks file data.
- Sentry per-instance ceiling 20 to 500/hr, breadcrumb trail restored
  (sanitized: urls/paths redacted, data payloads dropped), full stack
  paths kept; local vars, request bodies, and PII still dropped. Both
  api and web.

Honor ANALYTICS_ENABLED=false as an opt-out alias: it was documented on
the Docker Hub README but never wired in 2.x, so anyone who set it was
still tracked.

All capture stays behind the analytics opt-out gate.

tests/unit/api/deploy-mode.test.ts

@@ -0,0 +1,43 @@
+import { afterEach, describe, expect, it, vi } from "vitest";
+
+const mockExistsSync = vi.hoisted(() => vi.fn());
+
+vi.mock("node:fs", () => ({
+  existsSync: mockExistsSync,
+}));
+
+import { deployMode } from "../../../apps/api/src/lib/deploy-mode.js";
+
+describe("deployMode", () => {
+  const origEmbedded = process.env.EMBEDDED_MODE;
+
+  afterEach(() => {
+    if (origEmbedded === undefined) delete process.env.EMBEDDED_MODE;
+    else process.env.EMBEDDED_MODE = origEmbedded;
+    mockExistsSync.mockReset();
+  });
+
+  it("returns embedded when EMBEDDED_MODE is set", () => {
+    process.env.EMBEDDED_MODE = "1";
+    mockExistsSync.mockReturnValue(false);
+    expect(deployMode()).toBe("embedded");
+  });
+
+  it("returns external when /.dockerenv exists and EMBEDDED_MODE is unset", () => {
+    delete process.env.EMBEDDED_MODE;
+    mockExistsSync.mockImplementation((p: string) => p === "/.dockerenv");
+    expect(deployMode()).toBe("external");
+  });
+
+  it("returns native when neither signal is present", () => {
+    delete process.env.EMBEDDED_MODE;
+    mockExistsSync.mockReturnValue(false);
+    expect(deployMode()).toBe("native");
+  });
+
+  it("prefers embedded over external when both signals are present", () => {
+    process.env.EMBEDDED_MODE = "1";
+    mockExistsSync.mockReturnValue(true);
+    expect(deployMode()).toBe("embedded");
+  });
+});