Hi @Oleg Tserkovnyuk Glad to know you have identified the corresponding resource type and the RBAC permissions needed to enable the access.
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to accept the answer .
Issue:
Seeking to assign the minimum permissions needed to be assigned to the user to view API connection resources on the portal
Solution:
Assign the user Microsoft.Web connections read
permission to grant user just read permissions for API connection resources on the platform. Please refer the below image
If I missed anything please let me know and I'd be happy to add it to my answer, or feel free to comment below with any additional information.
I hope this helps!
If you have any other questions, please let me know. Thank you again for your time and patience throughout this issue.