In the new Site Builder Theme (Empire), it appears there are only pre-designed/default icons in the Icons & Text section. How do I go about added my own icon images?
There isn't a way to add your own icons in Site Builder at this point in time, sorry about that. One option would be to set up your own list of icons and text using the "Text & Media" section type. Or, if you're handy with code, you could add in your own icons by customizing your site theme (available on the Business plan and above).
Happy to help if you have any further questions at all.