Move functions from `experiments/` to `src/`

[juliasloan25]

We should minimize the code that's in experiments/ and instead have the bulk of our package in src/. For now we'll skip the component models, since that will be a large change on its own.

Files/functions to move now

Checkpointer module: #1612

• experiments/ClimaEarth/components/shared/restore.jl --> Checkpointer

Input module: #1613

• experiments/ClimaEarth/user_io/arg_parsing.jl --> Input
• experiments/ClimaEarth/cli_options.jl -> Input

SimOutput module #1617

• experiments/ClimaEarth/user_io/coupler_diagnostics.jl --> SimOutput
• experiments/ClimaEarth/user_io/benchmarks.jl --> SimOutput

Plotting extension #1621

• experiments/ClimaEarth/user_io/diagnostics_plots.jl
• experiments/ClimaEarth/user_io/debug_plots.jl
• experiments/ClimaEarth/leaderboard/ (data_sources.jl mostly dependent on component model-specific diagnostic names, but I think this is okay)
• experiments/ClimaEarth/user_io/postprocessing.jl (stub in src, extend in extension)
• experiments/ClimaEarth/setup_run.jl: postprocess(cs) (stub in src, extend in extension)
• experiments/calibration/run_calibration.jl: scatter_plot, param_versus_iter_plot (these depend on EKP too)
• experiments/ClimaEarth/leaderboard/: test_rmses.jl (and functions to get sim, obs dicts) --> SimOutput

SimCoordinator module (name?)

• experiments/ClimaEarth/setup_run.jl: run!(cs), step!(cs) --> SimCoordinator