Move node tests to integration tests where possible

[Wodann]

To improve encapsulation, we always try to only add functions in a scope if they're needed to expose some piece of private information. If a public API already exists that can be reused to create helpers functions, these helpers functions should exist outside the original encapsulation (e.g. mod, enum, trait, or struct).

When writing tests, we follow the same principle: If a test can be written using the public API of the crate, they should be in the tests folder, instead of being included in the same file.

Definition of Done

• Move the tests containing only calls to the public APIs of Node to the tests folder

Depends on

• https://github.com/NomicFoundation/edr/issues/224