Is it "Element Catalog", "Component library" or "Element Library"?

We use it somewhat interchangeably, there is some ambiguity it seems. Grepping "Element catalog" in monorepo yields a couple of results. Also "catalog" in general (installation dialog) yields more results.

Since we call the API addElementLibrary already, I suggest that we standardize on "library" over "catalog"

We also use the term "component library": https://remotion.dev/docs/studio-protocol/component-library-integration