i added google api but the button save option not working

This plugin will disable the save button if there is currently an active pagespeed scan running. Are you able to verify if that is the case?

There should be a status near the top of any of the plugin pages that allows you to see if a scan is running, and cancel it. Of course by time you read this it will probably have ended on its own if there was a scan running.

If that doesn’t sound like the source of your issue, can you check your browser inspector console and let me know about any JS errors listed there?