feat(deps): @sentry/nextjs error tracking (DSN-gated, dormant by default)

Wires the Sentry SDK shipped-but-dormant: no-op unless
`NEXT_PUBLIC_SENTRY_DSN` is set in the environment. Production opts
in via the deploy env; dev + CI stay quiet.

- `sentry.client.config.ts` / `sentry.server.config.ts` /
  `sentry.edge.config.ts` — runtime init, each guards on the DSN.
- `instrumentation.ts` — Next 13.4+ instrumentation hook that lazy-
  imports the server + edge configs when the DSN is present.
- `next.config.ts` — withSentryConfig only wraps the config when
  the DSN is set, so dev builds skip source-map upload + middleware
  injection.
- `src/lib/env.ts` — added optional NEXT_PUBLIC_SENTRY_DSN +
  SENTRY_ENVIRONMENT + SENTRY_TRACES_SAMPLE_RATE (defaults to 0.1).

Env vars to add to .env.example (blocked from this commit by the
.env hook — apply manually):

    # Sentry (optional — SDK is a no-op without a DSN)
    NEXT_PUBLIC_SENTRY_DSN=
    SENTRY_ENVIRONMENT=
    # Defaults to 0.1 (10%) when unset
    SENTRY_TRACES_SAMPLE_RATE=

Replay is opt-in only — disabled by default for now; we'd need to
audit privacy implications (PII redaction, GDPR) before enabling it.

Verified: tsc clean, vitest 1315/1315, next build green with DSN
unset (Sentry plumbing intact, runtime no-op).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

package.json

@@ -55,6 +55,7 @@
     "@radix-ui/react-tooltip": "^1.2.8",
     "@react-email/components": "^1.0.12",
     "@react-pdf/renderer": "^4.5.1",
+    "@sentry/nextjs": "^10.53.1",
     "@socket.io/redis-adapter": "^8.3.0",
     "@tanstack/query-broadcast-client-experimental": "^5.100.10",
     "@tanstack/react-query": "^5.100.10",