One master dataset, report unique datasets, both?

Hats off to you for doing the work of a whole team of data stewards.  You will want to consider including others in your company in this curation work and establish a data dictionary culture, data stewardship, and maintenance.

Best practices depend on the company size, the variety of data subjects, and the egos of the individual teams when it comes to subject matter expertise ownership.  Your current approach seems to be well suited to smaller sized enterprises.

For multi field table joins you can use composite keys or the custom generator functions in Power Query.