Here a tutorial for adding font families to theme.json. I know for awhile you couldn’t add it in the setting section of theme.json. But, It looks like that might have changed now.
There is also a style section that you can use to drill down into different blocks and assign font families there. I haven’t really created any themes in over a year now. So I’m a little behind changes that have been made.
Also keep in mind that you can assign font-families by css. If you have an older theme with custom css it might have a rule to override your default font-family. Try looking through the tutorial first and see if it help you to identify where the problem might be.