How does privatelink work under the hood with hyperplane and blackfoot edge devices?

Question

I know the basics of privatelink and how it creates an ENI inside the VPC which can be resolved from a service outside the VPC.

I want to understand how it truly works under the hood by steps, but can't wrap my head around it all.

After digging, I found this talk https://www.youtube.com/watch?v=8gc2DgBqo9U, but I can't organize all the steps that actually happen easily.

So how I see it is,

1. The VPC creates the ENI
2. To talk to another service, it goes through "the AWS network(I don't know how exactly)" which decides that's a hyperplane node job (somehow)
3. Hyperplane then routes that to the blackedge devices, who gets the physical info of the src/destination and makes the connection

There are a lot of incomprehension and blackboxes in how I explain it, because it's still vague to me. It looks like it's "private" but only on the software level, but it is privately public inside the AWS network.

Thanks for enlightening me.