Does CPA matter for a Engagement campaign?

Short answer: not really, and here’s why
Nothing is being ‘acquired’ in an Engagement campaign, there's no sale or lead being optimized for, just interaction with the content itself. Trying to calculate a cost per acquisition here is measuring something the campaign was never built to produce.
Ask your agency this instead

Want the metrics that actually matter for a Engagement campaign? Open the tool and pick one.

Other metrics for a Engagement campaign
Sources

Adamigo provided the Engagement-objective CTR, CPC, and CPM figures used here, along with explicit engagement-rate tier language that informed how the bands were set.