Small simplification: Reuse the activity we looked up elsewhere.
Write to FS from the caching module.

[#67856314]

https://www.pivotaltracker.com/story/show/67856314
Cache entries after successful authoring.
Rename caching module to sg_activity_caching.rb rename some methods too.

json_cache_path ➙ cache_path(filename)

Should finish [#67856314]
https://www.pivotaltracker.com/story/show/67856314