Improve error logging

[RemiBardon]

After we Implement proper request tracing, we should improve how errors are logged and handled. We've already done one pass by implementing custom error codes and migrating to thiserror but the API we did end up with could still benefit from a lot of improvements.

Here are some great resources regarding the subject:

• Rust web frameworks have subpar error reporting | Luca Palmieri
• Error Handling In Rust - A Deep Dive | Luca Palmieri
• Fast and flexible observability with canonical log lines | Stripe Blog

Those are about Axum more specifically:

• Fallible handlers for custom rejections · Issue #2965 · tokio-rs/axum
• Can we take inspiration from how Pavex handles errors? · Issue #2587 · tokio-rs/axum

And this is an interesting replacement for anyhow (fork with additional features):

• eyre: A trait object based error handling type for easy idiomatic error handling and reporting in Rust applications | crates.io