[Request]: Redesign error handling

### Feature description

Redesign error handling:
* Error types modeled around units of fallibility (single operations that may
fail)
* must be extensible (#[non_exhaustive] for the win)
* should be very conscious of their public surface

For a more in-depth study deep dive into [this blog post](https://sabrinajewson.org/blog/errors) or [this gists](https://gist.github.com/quad/a8a7cc87d1401004c6a8973947f20365) that goes through the same post but with an emphasis on `thiserror`.

### Motivation

TODO

### Requirements

TODO

### Open questions

_No response_