The Design Studio is basically a cached version of what is in the Web Template. Web Pages etc etc tables that you see in the Power Pages Management App.
If you make a change directly from the Power Pages Management App and you have the Designer open, then you need to re-Sync from inside the designer - to pull your updates into the Designer.
Similarly, you can make changes in the Code Editor (VS Code online) within the Designer - typically when you do this you will be prompted to sync the changes. If you open the code editor for the Web Page in the designer, you will find the other objects like Web Templates etc in the left hand column.
One thing you have to watch out for when working in both the Designer & the Management App at the same time is Autosave. As you can make a change from the Management App, save it, and then touch something in the Designer and overwrite your change as the designer autosaves on every update. Similar issues can arise (but less frequent) if you leave the item open in the Management App, whilst and after making changes in the designer,