will deauthorizing my Macbook delete data/playlists/library from Apple Music

Authorizing your Macbook should not alter anything. Deauthorizing can potentially have an impact if you are using either the iTunes Match or Apple Music subscription services. In particular downloaded Apple Music subscription content in the library may be invalidated and/or removed automatically.

You've mentioned both authorizing and deauthorizing. Are you planning to use a different ID? If so review Authorization vs. association - Apple Community first.

tt2

I see. If your computer isn't currently authorized then you won't have Sync Library enabled, or at least it won't be showing your cloud content right now. To see your iCloud Music Library the computer needs to be authorized to your Apple ID, you need to be signed into your Apple ID in Music, and the computer will become associated with your account when the iCloud Music Library is made available. Local content should be absorbed into your iCloud Music Library once you enable Sync Library (see Use Sync Library with your Apple Music subscription - Apple Support).

If you want to keep the local library and the cloud library separate for reasons see Use multiple libraries in Music on Mac - Apple Support and make a new separate library for connecting to your Apple Music subscription before you enable Sync Library.

Ideally you would have a complete backup of your library and media on a separate external drive so that original songs or playlists can always be recovered in the event that you delete something in error.

tt2