SQLite is frequently used as a local database in mobile phone applications. This is great for persisting data that doesn't need to go over a network or the Internet.
Making a mobile phone application that talks with a web application is very common too. Having a MySQL database connected to that web application is also very common. A delegated connection to a database is roughly what most websites do whether the client is a web browser, a human, or the client is a mobile application.
There are some tools such as GraphQL that provide a very generic HTTP-based API to access an underlying database. These could be useful for you too.
Using MySQL directly in a mobile application would be incredibly weird, though. I found this Android application that can connect directly to a remote MySQL server:
https://play.google.com/store/apps/details?id=net.probytion.mymoclient&hl=en Incorporating that functionality directly within your Android application would be very unusual and probably not the best approach.
The question and answer here offers some more detail about connecting a mobile phone application directly to a MySQL server: