ci: add Node.js version matrix, caching, and lint step to test workflow

## Problem

The CI workflow at `.github/workflows/test.yml` has several gaps:

1. Only tests on Node.js 22.x (volta config says 16 — mismatch)
2. No dependency caching between runs (slow CI)
3. No lint step in CI (eslint only runs via pre-commit hook)
4. Uses `actions/checkout@v2` and `actions/setup-node@v2` (both outdated)

## Suggested Fix

```yaml
jobs:
build:
runs-on: ubuntu-latest
strategy:
matrix:
node-version: [18.x, 20.x, 22.x]
steps:
- uses: actions/checkout@v4
- uses: actions/setup-node@v4
with:
node-version: ${{ matrix.node-version }}
cache: 'yarn'
- run: yarn install --frozen-lockfile
- run: cd packages/web && yarn build
- run: cd packages/web && yarn lint
- run: cd packages/web && yarn test --verbose --maxWorkers=2
```

## Severity

Medium — CI reliability and speed

Start with .github/workflows/test.yml and inspect the existing test job, then compare its Node.js version with the Volta configuration mentioned in the issue. Update the workflow to cover the requested Node.js versions, dependency caching, current action versions, and the web lint command; run the workflow or its equivalent checks to confirm build, lint, and tests pass for every matrix entry.

索引モデルが issue の本文から書いたものです。