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.

apps/api/src/lib/system-info.ts

@@ -0,0 +1,23 @@
+import { existsSync } from "node:fs";
+import os from "node:os";
+import type { InstanceStartedProperties } from "@snapotter/shared";
+import { deployMode } from "./deploy-mode.js";
+
+// Facts about the running instance, shipped once at boot as the
+// `instance_started` analytics event. Returning the shared event-property type
+// keeps this gatherer in lockstep with the event contract (single source of
+// truth) rather than duplicating the shape here.
+//
+// The NVIDIA Container Toolkit exposes GPU device nodes when a GPU is passed
+// through (docker run --gpus / compose deploy.resources.reservations), so a
+// filesystem check is enough; no nvidia-smi spawn or AI dispatcher needed.
+// This is deliberately independent of packages/ai's isGpuAvailable(), which
+// only reflects hardware in use by an already-started dispatcher.
+export function gatherSystemProperties(): InstanceStartedProperties {
+  return {
+    arch: process.arch === "arm64" ? "arm64" : "amd64",
+    os_platform: os.platform(),
+    deploy_mode: deployMode(),
+    gpu_present: existsSync("/dev/nvidia0"),
+  };
+}