Why navies test new machinery in small ships

Were prototypes usually tested in small ships before the idea moved to a larger scale?

Yes. A failed tug or sloop was far easier to absorb and explain than an unsuccessful capital ship costing the modern equivalent of billions.

Navies normally tried unfamiliar machinery in a small vessel before scaling it up. A tug or sloop limited the money, manpower, and political credibility exposed to failure. If the experiment performed badly, officials still retained a usable minor vessel rather than an enormously expensive fleet unit. Prototype size was therefore a procurement-risk decision as much as an engineering choice.