Steps
Go to the Create (or Edit) Contact Form page
In the left panel (called Available Fields) start typing the name of the Category field to search for it - DO NOT PRESS ENTER
To speed up your filtering: use the filters to turn off the other types of fields so you’re only seeing List fields
This will reduce the Category fields available
Press the green Tick symbol that is next to the List field you want to add
It will appear on the right side
Scroll to the bottom and press Save