Does user need Programmatic Access if using EC2 Instance Connect service?

I think you're confusing two different connections.

SSH is for accessing the operating system of that instance... you don't need any special access rights within AWS for that -- other than you need access to the virtual private network that the instance is in. Otherwise, if you have the SSH key and the user to login - you're done.

The "IAM" and "AWS CLI" are ways of interacting/CRUD (create, read, update, delete) with the "objects" within the account. These include spinning up a new instance or creating a new subnet, changing the parameters of a dynamic group, many many many others. Neither IAM (what rights an AWS user has over which objects) nor the AWS CLI give you access to the operating system of a EC2 instance by themselves.