On the Mac, when you launch Pages and open a new document, the first thing you should do before entering any content is manually Save (or option+Save As…) that Pages document to one with a real name, not Untitled n. After the first save, autosave is enabled (there is no user interface to autosave). Once a Pages document has been saved and you close the document and quit Pages, reopening that document enables autosave as it is remembered.
You want to save and preferably close that Pages document on the Mac before beginning to work on it from your Phone. In the past, I have not done that and opening it on an iPad in Pages, and making changes on the Mac would after a slight network delay, update the content on the iPad. Haven't tried this in a long time and it may not work that way now.
In order to synchronize content between macOS and i/Pad/OS you need to be saving the document to iCloud Drive, and in macOS Ventura through Tahoe, visit System Settings > Your name avatar > iCloud panel. Observe the Saved to iCloud section and click [See All]. On that displayed panel, you should have the following enabled:
- iCloud Drive
- Passwords & Keychain
- Pages
- System Settings
and click Done.
This now reveals a Pages folder on iCloud Drive that can be seen by Pages on the Mac and phone/iPad. Your documents will now synchronize. The side-effect on the Mac is that instead of a first launch Template Chooser, you will see a File Chooser instead. If you want to start a new document on the Mac, then you choose File > New… and that pops the Template Chooser.