The Agile way is more the other way around:
- Single feature/screen/part in mobile app (Should create user value, can you make it smaller?)
- Question what serverside API is minimally needed to implement this part of the app
- Question what minimal database structure is needed for this part of the API
This comes from the Agile XP practice YAGNI (You aren't gonna need it).
Work on things you need now and not what you think you might need. This increases learning you get from earlier finished parts. Also you should work on implementing complete features that give user value. Users might start using the product already when just 10% of the features are implemented (for example), because it already leads to actual usage value.
If you give the working app to your clients regularly as one of the Agile principles says,
Deliver working software frequently, from a couple of weeks to a
couple of months, with a preference to the shorter timescale.
then requirements will change and you might not need all the database structures you envisioned at the start for example.
My favorite Agile principle:
Simplicity--the art of maximizing the amount of work not done--is