Tunnel public hostname access control for not-browser HTTP clients (Java WebStart)

My application is Java based and it opens HTTP connection to a tunnel HTTP service published to a public hostname. I want to limit access to this application to specific Zero Trust users that are connected to WARP CLIENT in ZERO TRUST mode. But cloudscape always asks for browser authentication to the uses, no matter if such OS connections is active or not.

So, my Java-based app cannot access (as HTTP client) to that resources.

Is there a way to let a custom HTTP-based (not browser) application access to these public hostname services?