How to add more tags (folders) to my Pages app?

You do not add to the Pages application, but you can add Tags and create new document folders using either the Pages Save/Save As… panel or the FInder.

You have a conflict of terms in your post. Tags are a Finder feature that you can add to a Pages document when it is opened by clicking the document title bar and the drop-down panel will have a Tags: field. If there are no tags on the document, clicking once in that field will show a list of available tags defined by the Finder. Click one, and if you wish to add another, click in the Tags field immediately after the existing tag. Then click the title bar again to close that panel.

One can also add one or more tags via the Save/option+Save As… panels much as described above.

Pages remembers the folder where the last file was saved in future saves until you change that folder location. When you choose the File menu > Save for the first time, or option-key File menu > Save As… you will see the following:

The arrow symbol must be pointing upward that is adjacent to the location selector. That permits a full save panel view and the presence of a New Folder button at the bottom of the Save dialog. If you click that, you will have to navigate to where you want the new folder, give it a name, and then click Save to place your current Pages document into that new folder location. Or, you can use the Finder to create a new folder location and in your Save panel, direct Pages to that location in a Save/Save As panel and then save it there.