How to update Pages document from Mac to iPhone

If understood correctly, you want changes you make to the same Pages document on Mac and iPhone to automatically apply changes to both.

On the Mac, System Settings > [your name] > iCloud : Saved to iCloud : [ See All ] > Pages. Slide to enable Pages. Next, you copy the Pages document from your Mac to the iCloud Drive location in the Finder Window sidebar. Changes you make to the Pages document on the Mac will automatically synchronize across iCloud Drive, where you can open that document in Pages for iOS.

On the iPhone, you would visit Settings > [ your name ] > iCloud : Saved to iCloud : See All and Pages enabled there.

See Sync a Pages document across devices - Apple Support