refactor: decouple object methods into reusable primitives

[xavierdmello]

Decouples object methods into standalone primitives to enable usage in restricted environments without async and SystemTime, like ZKVMs. This allows critical functions (e.g., verify_update) to run in synchronous ZK proving environments, facilitating on-chain verification of beacon chain state.

[ncitron]

This is a great start! My comments focus on two main areas.

1. Avoid SP1 specific functionality. We want to ensure any prover can use this and would like to stay neutral. Because of this I don't love the SP1 patched crates being directly by Helios.

2. Increasing the size of the common crate. If the major goal here is just to have access to the core consensus functions in a separate crate, I think the best way to do so would be by moving those into some new consensus-core crate and deeply assess how to avoid dragging things out of config and execution into this new crate or common.

[ncitron]

This is looking really good. Left a few comments and questions and think we should be good to merge after these things have been addressed.

Also can you address the fmt and clippy issues we are running into in CI?

[xavierdmello]

Addressed comments & CI. One notable change was going from .clone() to clone_from() to make clippy happy here: https://github.com/succinctlabs/helios/blob/6e0e4f122038d8b570f9c5af9a834c79ec597c29/consensus-core/src/consensus_core.rs#L149-L155

[ncitron]

LGTM! Amazing work!