feat(experiments): Implement `run_experiment` (#3471)

* Sketch out run_experiment

* Make evals required

* Correctly use example protocol

* Set up full end-to-end clientside testing and write experiment test

* Clean up type annotations

* Ruff 🐶

* Update type annotations for evals

* Clean up experiment runner

* Fix syntax error

* Revert evals changes

* Restore deleted space

* Use independent rate limiters

* Do not explicitly import `run_experiments` at the top level

* Rename type annotations for domain-specificity