Improve miden-tx-prover error handling

[SantiagoPittella]

What should be done?

As the error cases in the prover and proxy kept growing, using String as error type is no longer suitable. We should implement an error type, following the standards across miden's repos to facilitate the usage of the CLI.

How should it be done?

A new error enum should be in place, and we should use thiserror like in other miden's crates.

When is this task done?

The task is done when the functions and methods that uses String as error type are replaced with an error from the new enum.

Additional context

No response

[SantiagoPittella]

We might use this issue to improve a bit documentation and comments that are now outdated. Like: #1014 (comment)

[bobbinth]

Closed by #1038.