No (Pushover) push notifications on Mac

Is anyone using Pushover for Desktop on macOS?

The mobile version has been working great for me for years, but I don’t get any notifications on my Mac (after having bought the deskop license on Black Friday and following the steps mentioned in their documentation).

What can be wrong? How to fix this?

(Yes, I have contacted their support, but their responses are slow and not helping so far)