All email sends work with Email Insights, even nested programs. As a test, I would run an email performance report and select the specific email asset from that nested program in the setup tab and define the send date. If results populate, then your filters in Email Insights need to be adjusted. If results do not populate, then you may have selected the incorrect send date range or the incorrect email asset.
Devraj, thanks for the response. I know that all emails should work with Email Insights, but that's clearly not the case. There were no filters in place for content/device/audience, and the date range in the screenshot would have captured the emails if Email Insights was capable of reporting on nested program engagement emails. If you have evidence of this working for you, I'd love to see it and compare.
Furthermore, our engagement-type programs are not populating in the Filter by Content search functionality (nor are the programs nested underneath showing up, nor are the emails in those nested programs or the smart campaigns used to send those emails), hence the inquiry as to whether this omission of Engagement emails is intended functionality or a bug to be submitted. Again, if you have evidence of these populating for you, please share!