What is the maximum number of concurrent sessions when using AWS Session Manager?

There is no definitive limit for the maximum number of sessions that can be established leveraging AWS Session Manager; and like you rightly stated in your question, there is no information regarding this in AWS' documentation. There are however a couple of factors that determine the number of sessions you are able to establish to an EC2 instance leveraging AWS Systems Manager. These include the bandwidth capacity available between the IAM user's device and the EC2 instance, the capacity of the EC2 instance Session Manager sessions are being initiated to, and the duration of the sessions initiated. Finally, you can have multiple IAM users establish sessions using AWS Session manager to the same EC2 instance concurrently. For more information regarding connecting to EC2 instances with session manager, kindly access the URL below.

https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/connect-with-systems-manager-session-manager.html