Add CI workflow to build backend and web frontend

[Jacobcdsmith]

Problem

There’s a local post-merge script and a build step for web/, but no CI workflow to build/test on push/PR.

Proposal

Add a GitHub Actions workflow that:

• Runs npm ci, npm run build in the repo root
• Runs npm --prefix web install and npm --prefix web run build
• Runs tests (npm test)
• Triggers on push and pull_request events
• Optionally uses a node version matrix (Node 18, 20)

Benefits

• Prevents broken builds from being merged
• Ensures frontend dist is buildable in CI
• Catches TypeScript errors and test regressions early