Jetpack not connecting despite WordPress.com dashboard saying it has

If I click the Connect Jetpack button the Completing Connection page shows up saying I’m connected.

I click the Return to your site button (which btw way needs renaming because that is false) which sends me to the Jetpack plans page (not my site see?).

Clicking Free at last sends me back to my Dashboard but the Connect Jetpack button is still displayed (refreshing the page makes no difference either).