When we create a VPC, we generally allocate it a private IPv4 address range as specified in RFC 1918.
I am making an assumption that Internet Gateway, NAT Gateway etc. are hosted on AWS managed VPCs as they are highly available and scalable same like how a customer would design a service on AWS.
Are there private IPv4 ranges AWS reserves for its use to solve overlaps between Customer's VPC and their own VPCs that hosts Internet Gateway / NAT Gateway? How is the CIDR overlaps managed?
It appears that you are asking about overlaps between customer VPCs and the actual networks used to 'run' AWS. However, there is no such overlap.
All networking in VPCs is virtual. Infrastructure deployed within VPCs are given IP addresses from the VPC's CIDR range. For example, a NAT Gateway connects to a VPC via an Elastic Network Interface (ENI), which consumes a private IP address from within the VPC. This allows it to communicate with other resources in the VPC, such as EC2 instances, RDS databases and Load Balancers.
The Internet Gateway does not consume any private IP addresses. It is simply a routing concept between a VPC and the Internet.
The actual equipment that AWS uses to operate services runs on separate networks that exist 'outside of' VPCs.