I solved a problem posting images using wordland.social. To do so, I used a kind of "random walk" to get there, so I didn't remember which of several things I did that made it work. I subsequently went back and found how to do it "officially".

To enable the JSON API within Jetpack:

1. Go to Jetpack > Settings
2. Scroll to the bottom to find the Modules link in the footer
3. Scroll through the list to find the JSON API
4. Activate it

This is described here: https://jetpack.com/support/control-jetpack-features-on-one-page/