test(web): setup Vitest and add unit tests for lib utilities and auth store

[docile-imbereyemaso]

Summary

Establishes a testing floor and baseline test suite for the apps/web workspace using Vitest.

Specifically, this PR:

• Installs Vitest as a dev dependency in apps/web.
• Adds the test script (vitest run) to apps/web/package.json.
• Adds unit tests for pure utility functions in lib/format.ts and lib/metrics.ts
• Adds unit tests for the session state machine in stores/auth.ts.
• Adds a Test web step to .github/workflows/node.yml to enforce web test verification on PRs.

Type of change

• Bug fix
• New feature
• Refactor / cleanup
• Docs
• Infrastructure / CI
• Breaking change

Areas touched

• apps/server (NestJS)
• apps/web (React / Vite)
• apps/agent (Go)
• packages/protocol (shared WebSocket contracts)
• infrastructure / .github/workflows
• docs

Related issues

Closes #55

How to test

1. Run npm run test --workspace=@docksight/web locally.
2. Check the CI checks on this PR to confirm that the Test web step in .github/workflows/node.yml executed and passed.

Checklist

• Change is focused and stays within the existing modular monolith boundaries.
• Ran the relevant checks locally (see below).
• Updated docs under docs/ if module boundaries or the protocol changed.
• Added an ADR under docs/decisions/ if this is a larger architectural change.

Local checks

# packages/protocol must be built first — apps/server and apps/web
# import it from its dist output.
npm run build --workspace=@docksight/protocol
npm run test  --workspace=@docksight/protocol

npm run build --workspace=@docksight/server
npm run lint  --workspace=@docksight/server
npm run test  --workspace=@docksight/server

npm run build --workspace=@docksight/web
npm run lint  --workspace=@docksight/web
npm run test  --workspace=@docksight/web