Create VPC Endpoint Service:

In the shared VPC, create a VPC endpoint service using the Network Load Balancer (NLB) that fronts the centralized application.

Enable the option to require endpoint acceptance to control which business unit VPCs can connect to the service.

Set Up VPC Endpoints in Business Unit VPCs:

In each business unit VPC, create a VPC endpoint that points to the VPC endpoint service created in the shared VPC.

Use the service name of the endpoint service created in the shared VPC for configuration.

Accept Endpoint Requests:

From the VPC endpoint service console in the shared VPC, review and accept endpoint connection requests from authorized business unit VPCs. This ensures that only authorized VPCs can access the centralized application.

Configure Routing:

Update the route tables in each business unit VPC to direct traffic destined for the centralized application through the VPC endpoint.

This solution ensures secure, private connectivity between the business unit VPCs and the shared VPC, even if there are overlapping CIDR blocks. It leverages AWS PrivateLink and VPC endpoints to provide scalable and controlled access​(AWS Documentation)​​(Amazon Web Services, Inc.)​.