Lambda to VPC connection invisible

Hello.

After I connect a Lambda to a custom VPC from Management Console -> Lambda Screen -> Configuration -> VPC

I think your settings are correct.
Connecting Lambda to a VPC does not create a VPC endpoint.
If you have configured it correctly, check the ENI from the EC2 console and the Lambda Hyperplane ENI should have been created.
https://docs.aws.amazon.com/lambda/latest/dg/configuration-vpc.html#vpc-configuring

An interface type of "lambda" will be created as shown below.

Access resources within the VPC via this created ENI.
https://docs.aws.amazon.com/lambda/latest/dg/foundation-networking.html#foundation-nw-connecting

Lambda accesses resources in your VPC using a Hyperplane ENI. Hyperplane ENIs provide NAT capabilities from the Lambda VPC to your account VPC using VPC-to-VPC NAT (V2N). V2N provides connectivity from the Lambda VPC to your account VPC, but not in the other direction.