There is a description of the deprecation behavior in the FAQ:
https://learn.microsoft.com/en-us/azure/information-protection/faqs#classic-client-deprecation
"After deprecation, the client will continue to work as expected. However, administrators will not be able to update policies on the portal, and no more fixes or changes will be supplied for the classic client."
So you can continue to use the classic client, but you won't be able to create, edit, or delete labels and label policies in the portal.
I'm checking about your question about the unified labeling and will follow up on this thread as soon as I have an answer.
Let me know if this helps answer your question.
Marilee