Remove most old example code

[PhilipFackler]

Description

Remove example code that duplicates what the DynamicSimulation app does

Closes #390 (indirectly)

Proposed changes

• Add existing "tiny" cases to CaseFormatTests to check JSON parser
• Remove example source code
• Create ref.csv files for cases that were still using the .hpp data
• Create .solver.json files where needed
• Update tests and input/output files to use same naming conventions

Checklist

• All tests pass.
• Code compiles cleanly with flags -Wall -Wpedantic -Wconversion -Wextra.
• [N/A] The new code follows GridKit™ style guidelines.
• [N/A] There are unit tests for the new code.
• [N/A] The new code is documented.
• The feature branch is rebased with respect to the target branch.
• [N/A] I have updated CHANGELOG.md to reflect the changes in this PR. If this is a minor PR that is part of a larger fix already included in the file, state so.