fix: restore cache service on PM2 restart

[pastelsky]

Root cause

Production cache writes were failing because PM2 was configured with ./cache-service/index.js, but the repository only contains cache-service/index.ts. PM2 omitted the cache service during restarts, leaving port 7001 closed while the main app continued running.

Changes

• point PM2 at the tracked TypeScript cache-service entrypoint
• enable Node type stripping for that process
• add a process-contract integration test that parses every PM2 entrypoint, checks scripts exist, validates TypeScript runtime flags and syntax, and starts the configured cache-service command to verify it listens on port 7001
• run the new test through the existing CI test command without changing workflow files

Verification

• node --test scripts/validate-process-config.test.mjs
• yarn format:check on changed files
• yarn typecheck
• yarn build
• pre-commit hook passed with existing repository lint warnings

The PR is not deployed.

[pastelsky]

Test using normal jest tests.