how to know windowed apps/stage manager is on

No there is not. However you can configure your app's windows to work together with Stage Manager when it is available. For some recommendations for working with Stage Manager, please see What's new in AppKit

If you'd like us to consider adding a way to tell when Stage Manager is active, please file an enhancement request using the Feedback Assistant. If you file the request, please post the Feedback number here so we can make sure it gets routed to the right team.

If you're not familiar with how to file enhancement requests, take a look at Bug Reporting: How and Why?