Google Apps Script code to send you an email every time a Google Analytics 4 property has a new referrer. Full instructions at https://ithoughthecamewithyou.com/post/email-alerts-for-new-referers-in-google-analytics-using-apps-script

Code.gs

var PropertyId = '';
var PropertyName = ''
var SendEmailTo = '';  

function main() {
  var scriptProperties = PropertiesService.getScriptProperties();
  var currentProps = scriptProperties.getProperties();
  var anythingNew = false;
  var newText = '';

  const metric = AnalyticsData.newMetric();
  metric.name = 'totalUsers';

  const dimension = AnalyticsData.newDimension();
  dimension.name = 'pageReferrer';

  const dateRange = AnalyticsData.newDateRange();
  dateRange.startDate = 'yesterday';
  dateRange.endDate = 'yesterday';

  const dimensionfilter = AnalyticsData.newFilterExpression()
  dimensionfilter.filter = AnalyticsData.newFilter()
  dimensionfilter.filter.fieldName = 'sessionMedium'
  dimensionfilter.filter.stringFilter = AnalyticsData.newStringFilter()
  dimensionfilter.filter.stringFilter.value = 'referral'

  const request = AnalyticsData.newRunReportRequest();
  request.dimensions = [dimension];
  request.metrics = [metric];
  request.dateRanges = dateRange;
  request.dimensionFilter = dimensionfilter;

  const report = AnalyticsData.Properties.runReport(request,
        'properties/' + PropertyId);

  if (!report.rows) {
    Logger.log('GA returned no data.');
    return;
  }

  for (var i = 0; i < report.rowCount; i++){
    var referrer = report.rows[i].dimensionValues[0].value;
    if ((referrer) && (referrer.length > 0)) {
      if (!(referrer in currentProps)){
          Logger.log('Found new referrer: ' + referrer);
          scriptProperties.setProperty(referrer, report.rows[i].metricValues[0].value);
          anythingNew = true;
          newText += 'New referrer: ' + referrer + '\r\n';
      }
    }
  }
  
  if (anythingNew) {
    MailApp.sendEmail(SendEmailTo, 'Found new referrers for ' + PropertyName + ' on ' + new Date(), newText);
  }
}