When uploading into the Media Library from the web console, you can ask for an "upload preset" to be applied with special settings for the uploaded content (e.g. incoming/eager transformations, moderation requirements, auto-tagging, etc.).
Such upload presets should be predefined in the upload settings page on your Cloudinary account.
Note that only signed upload presets can serve as the Media-Library default.
Within the upload preset's add/edit page you can configure different upload options such as: folder & public ID settings, allowed & target formats, incoming & eager transformations, and different add-on settings (Some additional preferences are available under "Advanced Options").
Don't forget to save the upload preset ("Save" button on the bottom right corner).
Now you can go and select the new upload preset to handle Media Library uploads by selecting it in the "Media library's upload presets" pull-down menu. An upload preset is selectable for Image, Video, and Raw file formats.
Make sure to save these settings as well ("Save" button on the bottom right corner).
And you're good to go!