No Linux Connectivity Client for non-HTTP Access Support?

You are correct that AWS Verified Access Connectivity Client, which enables secure access to non-HTTP(S) resources, is currently only available for Windows and macOS operating systems. Based on the available information, there is no Linux client available at this time.

The documentation specifically mentions support for "Windows and macOS clients at the time of this writing" when discussing the Verified Access Connectivity Client application. The download options listed in the documentation only include versions for "Mac with Apple Silicon," "Mac with Intel," and "Windows" for both the 1.0.0 and 1.0.1 releases.

There is no explicit mention in the provided sources about plans to release a Linux version of the Connectivity Client in the future. The documentation does not include any "coming soon" notices or explicit statements about Linux not being supported. This lack of information about Linux support is indeed a gap in the documentation clarity.

If Linux support is critical for your use case, you might want to contact AWS Support directly for the most up-to-date information on their roadmap regarding Linux client support for AWS Verified Access.
Sources
AWS Verified Access now supports secure access to resources over non-HTTP(S) protocols (in preview) | AWS News Blog
Connectivity Client for AWS Verified Access - AWS Verified Access
Secure Remote Access – AWS Verified Access Pricing – AWS