Is internal network traffic sent to private subnets via their NAT Server?

I'm wondering how resources in my public subnets communicate with those in my private subnets - when there is a NAT service present.

My impression is that a self-managed NAT Server obscures all private assets (resources we own) and all external communication is initiated by the NAT server, which is doing the “address translation.” Having private subnets without any NAT Server (managed as NAT Gateway or otherwise) and applying arbitrary IPs from the RFC ranges is not the same as having those ranges translated by the NAT Server (or NAT Gateway); the fact that the RFC ranges are canonically “private” is in no way enforced in that case, there’s nothing special about those typically private ranges. The full implications of that are not really clear to me, since it’s not something I’ve seen or used much.

Additionally, my impression is that a NAT server (managed or otherwise) and private IP ranges aren't just for protecting internal resources from external communications, and that even things inside my VPC's public subnets have to route through the NAT server. Anything that wants to send packets to those RFC ranges must first communicate with the NAT server, via its public IP given by the IGW. Thus the whole mechanism enforces routing through at least 2-3 AWS managed services, even for internal, public-private communications.

Is that (all?) correct?