You can try module Bulk Export, it does the same thing.
For json-ld, the best way is to use the api, available at url /api, it is a rest and json-ld api designed for that.
On Output Formats: this was released and we published the documentation and everything, and just forgot to register it so it would show up in the modules list. The original link you posted in your first message should work now.
Note: Output Formats just adds links to get these formats more easily, but it’s just using the API; both the standard JSON-LD output and the additional formats are native features of the API.