For web you can package Flet app to client-side (with pyodide, all Python logic runs in the browser, see an example here: https://gallery.flet.dev/todo/) and run as a server-side app (or server-driven) with Python logic running on the server (example: https://flet-controls-gallery.fly.dev/layout - notice faster loading compared to client-side one).
> If I'm writing Python that runs on the mobile device, it must talk to a server to read & write data. Doesn't this still require an API backend, database, cache, etc?
That's correct. Any backend service which provides Python API can be used when running Flet app on a mobile: FastAPI, Firebase, Supabase, Pocketbase, etc, but you use Python to call that which is awesome especially for beginner and non-web developers.
> It looks like Flet is for client-side code.
For web you can package Flet app to client-side (with pyodide, all Python logic runs in the browser, see an example here: https://gallery.flet.dev/todo/) and run as a server-side app (or server-driven) with Python logic running on the server (example: https://flet-controls-gallery.fly.dev/layout - notice faster loading compared to client-side one).
> If I'm writing Python that runs on the mobile device, it must talk to a server to read & write data. Doesn't this still require an API backend, database, cache, etc?
That's correct. Any backend service which provides Python API can be used when running Flet app on a mobile: FastAPI, Firebase, Supabase, Pocketbase, etc, but you use Python to call that which is awesome especially for beginner and non-web developers.