[Migration] Convert `/src/service` files to TS and ESM (API)

[jescalada]

We want to convert all the files in /src/service to TS and ESM imports.

This issue is part of the TS conversion Epic #23. I decided to split #19 into an extra issue since the proxy logic and the API are both rather massive.

Edit: Setting this aside for now; will continue once OIDC PR is merged.

Tasks

• Convert each file to TypeScript
• Manually test that features are working as expected
• Make sure unit tests/E2E tests are still working