I am using Pages v14.3 on macOS Sequoia v15.2. That version of Pages is supported on Sonoma and you should be using Sonoma v14.7.2.
If your Pages version is older, then this link to the Mac App Store will take you to Pages where you can update it. Right-click on that link and choose the Open Link in App Store menu item.
Your profile still shows macOS 14.5. Only if you are not currently running macOS 14.7.2, follow the next paragraph.
In System Settings > General > Software Update panel, if it shows Sequoia v15.2, look lower down on that panel and you may see a link named something like "Another update is available." If you click that link, it will open a new dialog showing the current version of Sonoma and probably Safari 18.2. When you choose to install these, you will get the Sonoma update, but not the Sequoia upgrade
When I use the File menu > Page Setup… panel to create a custom document size, and accept that change, the current Pages document automatically changes to that size. That is when I use File Menu > Save as Template… > Add to Template Chooser and give that new template an appropriate name that includes a specific page size. With that template created, I no longer need to care about selecting a page size as it is implicit in that opened template.
In reading your reply, I think you have created several templates that only confuse.
I always save my Pages templates to the Template Chooser, and not to another part of the filesystem outside of that chooser. I have never had Pages fail to save a template in this manner. Not all page sizes that one creates in the Page Setup screen become available in the Document panel selector either. That makes a saved template with the page size in its name even more important.
