Greenshift has several improvements in font management.
To use them, you need to assign fonts in Theme options to one of the available slots, then, assign a slot to Elements that you need.
First of all, visit Theme options

Here you can select System (default), Variable (Mona Sans), and also local. Greenshit theme has no own local font loader, but it uses font loader from Greenshift plugin Once you upload fonts in Greenshift, they will be available also in Greenshift theme selector.
These options allow to assign font to slot, but you need to assign slot to specific elements now
For this, use Style Editor when you are on Appearance – Site Editor mode

In Typography options you can assign your slots to elements. Also, there are options for separate blocks.
If you want to change also headings in content, then, you need to assign font also in Style editor – Blocks – Heading