fix(nextjs): build client analytics example with React 19.3

[jrandolf]

Root cause

Dependabot opened separate React and React DOM updates (#41, #42). Updating one alone can select incompatible peers, and the Next.js example is excluded from the pnpm workspace/CI. On the unchanged main SHA ad84d64fa949bc4fb28115688c5f440aa737d798, its production build fails while collecting page data: createContext is not a function. The server layout imports a client-only analytics provider.

Repair

• Update React and React DOM together to >=19.3.0.
• Move the analytics provider and GA script into an explicit client component, leaving the root layout on the server.
• Add the example's TypeScript dependencies and lockfile, and make its production build and audit part of CI.

Files: .github/workflows/ci.yml, examples/nextjs/app/{layout,providers}.tsx, examples/nextjs/{package.json,package-lock.json,tsconfig.json,next-env.d.ts}.

Local verification

All commands ran in an isolated external-drive worktree. hk check --all --slow, pnpm install --frozen-lockfile, pnpm build, pnpm pack --recursive --dry-run, pnpm typecheck, pnpm test, pnpm audit, actionlint, git diff --check, npm ci --ignore-scripts in examples/nextjs, npm run build there, and npm audit --audit-level high there each exited 0. Root command logs and exit codes: /Volumes/Code/Sources/.dev-storage/mathematic-inc-monitor/2026-09-25T1501Z-full.IgHeRG/logs/repairs/alyt-react/final/results.tsv; example logs: adjacent example-ci-{install,build,audit}.log. The unchanged-main example failure is captured in logs/native/alyt/example-baseline-build.log.

Merge gate

Do not merge until all exact PR-head strict checks, reviews, and ruleset conditions are green. The current default-branch SHA has successful Actions CI/hk/Analyze/gate contexts but is missing its strict GitHub Advanced Security CodeQL provider-57789 context; post-merge verification of that context remains an unresolved gate.