Organizational changes to shared CCE code

[knelli2]

Proposed changes

This is sort of just a mish-mash of various changes I've made while updating the ReduceCceWorldtube executable. Most of it is just clarifying/organizing code that's shared. Future PRs will make more substantial changes to ReduceCceWorldtube.

Towards #6246

Upgrade instructions

Code review checklist

• The code is documented and the documentation renders correctly. Run
  make doc to generate the documentation locally into BUILD_DIR/docs/html.
  Then open index.html.
• The code follows the stylistic and code quality guidelines listed in the
  code review guide.
• The PR lists upgrade instructions and is labeled bugfix or
  new feature if appropriate.

Further comments

[nilsdeppe]

LGTM, a few small suggestions you can squash immediately

[nilsdeppe]

You can squash immediately.

[nilsdeppe]

I think the CI clang-tidy is related to this include. I believe you don't actually need this in the hpp and can move it to the cpp, which should fix the issue.