See https://ithoughthecamewithyou.com/post/get-an-email-if-your-site-stops-being-mobile-friendly

MobileFriendly.gs

var urlToMonitor = '';
var alertEmail = '';
var runTestKey = '';

var runTestUrl = 'https://searchconsole.googleapis.com/v1/urlTestingTools/mobileFriendlyTest:run?key=';

function mobileFriendlyMonitor() {
  try {
    
    var postBody = {
      'url' : urlToMonitor
    };
      
    var options = {
      'method' : 'post',
      'contentType': 'application/json',
      'payload' : JSON.stringify(postBody)
    };
    
    var response = UrlFetchApp.fetch(runTestUrl + runTestKey, options);
    var json = response.getContentText();
    var mobileFriendlyResult = JSON.parse(json);
    
    if (mobileFriendlyResult.mobileFriendliness != 'MOBILE_FRIENDLY') {
      sendEmail('Mobile friendly test failed for ' + urlToMonitor + ', check https://search.google.com/search-console/mobile-friendly for details');
    }
      
  } catch (e) {
    sendEmail('mobileFriendlyMonitor failed for: ' + urlToMonitor + ' with error: ' + e.message);
  }
}

function sendEmail(msg) {
  MailApp.sendEmail(alertEmail, 'Mobile Friendly Monitor Alert on ' + Utilities.formatDate(new Date(), "GMT", "yyyy-MM-dd'T'HH:mm:ss'Z'"), msg);
}