New iPhone 16 is not syncing with my iPad Pro

These do not sync between devices. Photos, Notes, Reminders, Messages, etc.

Enabling iCloud for various functionalities such as Photos, Notes, Reminders, Messages, and more, as illustrated in the accompanying image, facilitates the seamless synchronization of each of these elements with iCloud through the internet.

If one of the devices is not connected to the internet then it may seem to you that they are not syncing. This link could assist you in pinpointing internet issues, a crucial step for synchronization. Internet not available WiFi and Cellular … - Apple Community

Note: If you delete any or all data from one device, it will also be removed from iCloud and all other devices linked to the same Apple ID. Likewise, the reverse is true as well.

Similarly...

These don't sync between devices Contacts, Calendars, Bookmarks, Notes, Voice Memos, shared photos, iCloud Photos, and emails. Each device syncs to the email account server which may be Google, iCloud, AOL, Exchange, Outlook, Yahoo, or any Other. Please see the pic below.

For Audiobooks, iMovie Project, and Apple Podcast log in with the same Apple ID as used in your Mac

If one of the devices is not connected to the internet then it may seem to you that they are not syncing. This link could assist you in pinpointing internet issues, a crucial step for synchronization. Internet not available WiFi and Cellular … - Apple Community

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