The latest version of MainWP v5.2 introduced REST API Version 2.
However, the old Version 1 keys have been inadvertently deactivated. We are working on a fix for this.
Creating a new REST API Key, and enabling the Legacy API credentials should help with connecting the browser extension again.
When creating a new key, keep in mind that you have to toggle on Enable MainWP REST API v1 Compatibility, and that you have to Save Settings for the key to be active and usable in the browser extension.