MQTT Startup Refactoring Part 1: core/ packages part 1 (#1728)

This PR specifically introduces a `core` folder and moves the following packages over, without any other changes:

- `api/backend`
- `api/config`
- `api/options`
- `api/schema`

Once this is merged and we confirm there's no regressions, I can migrate over the remaining changes piece by piece to split up application startup, backend services, http, and mqtt as was the goal of the earlier PRs!