I see the option. If you select a text layer, view it's properties, and then open the drop-down for selecting which font, the upload option appears in the lower left (I'll include a screenshot for reference). Note uploading custom fonts is a premium feature.
Hope that helps,
Unfortunately, I do not have an "upload" button like what is shown in your screenshot of the font drop-down menu. I do however already have "uploaded" fonts in the font drop-down menu that I am assuming were migrated to this version of Express from the original version since I originally uploaded the custom font files to a brand I created in the original Express. I'm looking into my account now to see if it is premium, but it is through an enterprise license.
Thanks for following up. I missed that you were using an enterprise type account. The process is slightly different for that type of account. For enterprise users, your Adobe account admin will need to add the required fonts for you using the admin console. They can follow the instructions here and once they do you will be able to find those fonts in Express: https://helpx.adobe.com/enterprise/using/custom-fonts.html