If you haven’t already, once you are logged into the Google console, then go back to your site in the same browser, then into the GD settings and into the Map settings and use the “Generate API” key button inside GeoDirectory settings to create a new key with all the necessary APIs. Of course you can create it in the same project where you have attached your billing account. If billing is setup correctly, the key will work. It may take a few minutes to work, but it will work.
Adding a restriction will not make it work, and may confuse things. I would wait until I saw it work, then add a restriction afterwards.
For the restriction, see: https://wpgeodirectory.com/docs-v2/integrations/google/#secure
http referrer
my-domain-name.com/*
However, you should follow the instructions in the console to add your restriction: https://developers.google.com/maps/documentation/javascript/get-api-key