Hey,
The website can use either DTM staging or Launch staging embed code. You can link DTM and Launch embed codes in production environment but similar is not available for staging. After upgrade to Launch, for staging you will have to use the Adobe Launch staging endpoint. It is not possible to link the legacy DTM staging endpoint to the Launch Staging Endpoint. So you will need to update the embedded code on your staging websites.
https://www.youtube.com/watch?v=4DyA1nqtgVg
Hope this helps!