I would reframe the question about the function of the bastion host. If the goal is to provide secure, access-controlled, audited accesses to remote hosts, then the use of Session Manager (or other features of Systems Manager) can accomplish those goals.
One of the primary benefits of using Session Manager is that it obviates the need to open up SSH or RDP, which reduces an environment's attack surface and simplifies the infrastructure by eliminating a bastion setup.
See this blog for details (although it pre-dates Session Manager): https://aws.amazon.com/blogs/mt/replacing-a-bastion-host-with-amazon-ec2-systems-manager/.
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