It varies. Sometimes it's just understanding enough about data to build data products. (Eg: a website with a recommendation engine component)

Knowing data visualization can also be useful.

Most deep learning companies focus on a particular application.

FWIW I'm actually self taught. I did client projects and learned machine learning on my own.

You could start by branching in to data engineering and understanding how data pipelines work. That's closer to the skills a full stack developer is likely to have.