I can't really offer an opinion as to why it is working like that without seeing how it has been set up.
Could we please get credentials so that we can have a look at this in the back end? (Preferably the staging site.)
I will mark your next reply as private to get the log-in credentials from you—you may want to create a temporary admin user for us to use that you can later delete. And be sure to have a current backup of your site.
The issue appears to be caused by one of your plugins specifically the wordfence plugin's firewall. It is blocking the API connections to google.
What I did was to set wordfence to Learning mode with an auto enable on the 23rd. Lets see if this option will identify the Google API connections as safe and allow it.
What I initially did on your test site was to disable all the non-toolset plugins. When I did this the issue wasn't present.
I began to enable the plugins one by one until I found that the Wordfence plugin was the cause. What you can try doing is to disable the wordfence plugin and check on the frontend.
If the map work you can then try to disable the firewall and enable the learning mode.
