[NETWORK] - Change `Result` return type in `ConnectedNetwork` trait to `anyhow`

[lukaszrzasik]

What is this task and why do we need to work on it?

The task is to migrate ConnectedNetwork trait to anyhow::Result return type.

What work will need to be done to complete this task?

No response

Are there any other details to include?

No response

What are the acceptance criteria to close this issue?

All the existing tests should still pass.

Branch work will be merged to (if not the default branch)

No response