How small could an aircraft-carrying cruiser be?

Did trials with aircraft catapults show that an Emerald-class cruiser was the smallest practical platform?

Not exactly: the trials showed the arrangement was awkward, while the smaller Arethusa class also operated aircraft and the Royal Navy settled on larger cruisers as the worthwhile operational platform.

The answer distinguishes the smallest ship that could carry an aircraft from the smallest cruiser on which the capability justified its cost and disruption. The Arethusa-class example undercuts a hard Emerald-sized threshold, while later Royal Navy practice favored larger cruisers as aviation and helicopter experiments evolved.