Thanks @Mickeybyte 

But in our case the native client tells me this in it's log when I try to connect (authentication in Azure with MFA done successfully):

2022-10-10T13:04:58.726+02:00 EROR (01) [libsdk] : Cdk::ErrorCallback:866: The task 'CdkGetConfigurationTask' failed with error: Your client was not launched with valid SAML2 credentials. Please contact your Administrator. (domain=55, code=3).
2022-10-10T13:04:58.752+02:00 EROR (01) [libsdk] : ServerErrorHandler::OnError:71: Handling error 'Your client was not launched with valid SAML2 credentials. Please contact your Administrator.' (domain=55(CDK_BROKER_ERROR), code=3) from task CdkGetConfigurationTask.
2022-10-10T13:04:58.752+02:00 INFO (01) [libsdk] : Server::HandoffToWorkspaceOne:1628: (26474C6C0D0) The server is in Workspace ONE mode: uag.corp.com/portal/nativeclient
2022-10-10T13:04:58.752+02:00 INFO (01) [ServerService] Handoff:1131 Handing off to https://uag.corp.com/portal/nativeclient
2022-10-10T13:04:59.146+02:00 INFO (01) [ServerService] Shutdown:213 The client is forcibly shutting down, clear all pending actions...
2022-10-10T13:04:59.147+02:00 INFO (01) [ServerService] Shutdown:228 The server https://uag.corp.com/ has no session. Will quit after logged out.
2022-10-10T13:04:59.147+02:00 INFO (01) [client] Disconnect:1205 The server https://uag.corp.com/ is disconnecting...

But the CS isn't:

If I continue with the HTML portal, the VDI opens without further authentication, hence SAML and TrueSSO works.

As we're on the latest versions of all components (client, uag, Horizon CS), and all configs are done "by the book", I guess this will end as a ticket with support. I really cannot see anything that should lead the client and/or CS to see this as Workspace ONE mode.