Transferring music from iPhone 16 Pro to Apple Music on MacBook Pro

See Authorization vs. association - Apple Community for some background on why creating a new Apple ID might not have been an ideal approach. Your past purchases are tied to your old ID. You may have locked your new device to your new ID. Updating apps on device works best when they are all purchased from the same ID.

See Move your iTunes/Music library to a new computer - Apple Community. You would ideally take this approach as opposed to extracting music from your device, but perhaps you no longer have that option.

If not, see Recover your iTunes library from your iPod or iOS device - Apple Community. The easiest method may be a temporary subscription to the Apple Music service, merging the music on the device into an iCloud Music Library which you then download to a computer and backup for security. Note however that Apple Music will reject purchases made by a different ID for your iCloud Music Library, reinforcing the earlier point that you should have stuck to your original ID. Perhaps it is not too late to go back to it?

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