Well it did for me and has for many other. Depends on exactly what you're doing. An in place upgrade from Mojave to Catalina or later should see the existing iTunes content automatically load into the relevant replacement apps. Should that fail you can try reconverting the iTunes Library.itl by option starting the Music or TV apps. Importing eligible local content into the other apps such as Books or Podcasts is more manual, but can be done. Your unhidden online purchase history remains available to stream or download to the respective apps. Note that video content can be withdrawn from the store by the rights holders without notice. For security you should maintain your own copies offline, or accept the risk that one or more titles might be removed over time if you don't want to dedicate storage and bandwidth to that. Upgrading to Big Sur won't of itself cause anything to be removed.
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