Thanks @jamie. The root issue is that my library removes tracks from playlists when running Core on the MBP. The full thread can be found here: Migrated Core, NAS Storage, Playlists Now (Mostly) Empty - #38 by noris
The title is a bit misleading because I didn’t actually migrate the NAS storage; the MBP is using the same NAS storage as the NAS Core is using (details in the thread). Thanks!