refactor(example): enhance example for public inputs validation

[IAvecilla]

Update the public input validation example to support both SP1 and Risc0 implementations. Additionally, improve the steps and documentation to make it easier to follow and execute.

How to test

You can test it locally following the commands in examples/validating-public-input/README.md or use holesky following the official documentation in docs/guides/3_validating_public_input.md.