Modernise old async code

This uses callbacks and I'd like promises and async/await: <paste>

Convert it, keeping behaviour identical:
- Errors that arrived as a first callback argument become rejections.
- Preserve the ordering. If operations ran sequentially, they must
  stay sequential — don't parallelise them as a "bonus".
- Anything that ran in parallel by accident, flag it rather than
  quietly changing it.
- Add the error handling the callback version was missing.

List every behavioural difference between the two versions, including
subtle ones around ordering and error timing.