ci(FR-2791): add backend.ai-client lint/typecheck/test/build workflow

[yomybaby]

Resolves #7198(FR-2791)

Epic: FR-2792 (backend.ai-client production readiness)

Summary

Adds a dedicated GitHub Actions workflow that validates packages/backend.ai-client on PRs and on main pushes. The repo's existing scripts/verify.sh only covers the React app, so library-only regressions (lint, typecheck, test, build) currently slip through.

Workflow

.github/workflows/backend-ai-client-ci.yml runs on PRs and pushes that touch the package or the lockfile, and executes:

1. pnpm install --merge-git-branch-lockfiles --no-frozen-lockfile (matches the vitest.yml pattern; the repo uses gitBranchLockfile: true)
2. pnpm --filter backend.ai-client run lint
3. pnpm --filter backend.ai-client exec tsc --noEmit
4. pnpm --filter backend.ai-client run test
5. pnpm --filter backend.ai-client run build

Path filter covers packages/backend.ai-client/**, pnpm-lock.yaml, and the workflow file itself; concurrency is set to cancel in-flight runs of the same head ref.

Soft dependency

The lint step depends on FR-2790 / #7204 landing first (that PR adds eslint.config.js). Both PRs are in the same Epic FR-2792 and intended to merge together; CI will be green on main after both land.

Out of scope

• npm publish workflow — separate ticket once a publishing strategy is decided.
• Coverage thresholds — separate ticket once additional unit tests land.
• Branch protection / required-check enforcement — left to the maintainer.

Verification

• YAML parses (python3 -c "yaml.safe_load(...)").
• All step commands run green locally on the merged-Epic state (lint 0 errors / 242 warnings, typecheck pass, tests 4/4 pass, build success).
• Action and pnpm versions (actions/checkout@v5, pnpm/action-setup@v5, actions/setup-node@v5, actions/cache@v5) match what's already used by vitest.yml and publish-backend.ai-ui.yml.

[yomybaby]

• ci(FR-2791): add backend.ai-client lint/typecheck/test/build workflow #7203 👈 (View in Graphite)
• main

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[Copilot]

Pull request overview

Adds a dedicated GitHub Actions workflow to validate the packages/backend.ai-client workspace package on PRs and on pushes to main, aligning the monorepo with package-scoped CI checks.

Changes:

• Introduces .github/workflows/backend-ai-client-ci.yml to run lint, TypeScript typecheck, tests, and build for backend.ai-client.
• Adds path-based triggers and concurrency cancellation to avoid redundant runs.