No file type option is showing in EXPORT

Have you scrolled down to the bottom of the dialog? File Settings are below Video, with further options below that.

You can collapse the sections of this dialog to take up less vertical room - click the triangular arrows.  Also you can save your own export preset, set up and named suitably for a certain purpose, and call that directly. Then you won't so often need to navigate these settings at all.

Rather than including any particular export destination into this preset - LrC can prompt you for that each time. Or it can save in the same place as the starting image. Optionally, into a defined subfolder name - which will be created as needed.