Hi @Jerzy Czopek Greetings! Thank you for posting this question on this forum.
Which APIM instance SKU should I choose
Based on the scenario you provided, the appropriate APIM instance SKU for VNET integration would be the Premium SKU. The Premium SKU provides advanced features such as multi-region deployment, autoscaling, and more advanced security features, which would aid in managing quotas and capacity for Azure OpenAI services across different environments. Please refer the documentation Automatically scale an Azure API Management instance which provides details on how you can implement Auto scaling for the APIM instance
How can I ensure that the environment VNETs can connect to APIM in the shared VNET?
Vnet peering should be enough to let APIM access the configured end points. Please take a look into the article Use a virtual network to secure inbound or outbound traffic for Azure API Management which provided different details on different approaches you can take to implement a Vnet with APIM as per your needs.
Will APIM be able to connect to the Azure OpenAI services using private endpoints effectively?
APIM uses a private IP address for a connection in the VNet or a peered VNet. Please refer the article section Routing for additional details on this.
The article Virtual network peering provides good pointer on Vnet peering can be achieved.
Hope this helps! Please let us know if you have any additional questions or need further assistance.