Assuming routing and everything else is setup properly I would suggest enabling VPC Flow logs with additional Meta-Data to find out what is being rejected in both the Source and Destination VPCs.
Knowledge center article for troubleshooting connectivity over VPC Peering.
VPC peering between Atlas cluster and AWSasked 21 days ago
Transit gateway & VPC peering - IP forwardingAccepted Answerasked 3 years ago
Accessing S3 Gateway VPC Endpoint from another VPC (VPC Peering established between both source and destination VPCs)Accepted Answerasked 2 years ago
VPC Peering and DNS resolution of a public Amazon Redshift clusterAccepted Answerasked 2 years ago
VPC peering and Network Firewallasked 7 months ago
Billing for cross-account VPC peeringAccepted Answerasked 3 years ago
OpenVPN client IP will not route accross VPC Peeringasked 6 months ago
ECS tasks stops server while connecting to mongo atlasasked 4 months ago
VPC peering with a VPC from a different AWS Organization - cost implicationsAccepted Answerasked 2 years ago
VPC Peering traffic volume mismatch between origin and destination VPCAccepted Answerasked 2 years ago