How to report console.error with Sentry?

As user @kumar303 mentioned in his comment to the question ... you can use the JS console integration Sentry.Integrations.CaptureConsole.

See https://docs.sentry.io/platforms/javascript/configuration/integrations/plugin/#captureconsole for documentation.

At the end you JS code to setup Sentry looks as follows:

import * as Sentry from '@sentry/browser';
import { CaptureConsole } from '@sentry/integrations';

Sentry.init({
  dsn: 'https://your-sentry-server-dsn',
  integrations: [
    new CaptureConsole({
      levels: ['error']
    })
  ],
  release: '1.0.0',
  environment: 'prod',
  maxBreadcrumbs: 50
})

If then someone calls console.error a new event will sent to sentry.

Here's a more robust override solution

// creating function declarations for better stacktraces (otherwise they'd be anonymous function expressions)
var oldConsoleError = console.error;
console.error = reportingConsoleError; // defined via function hoisting
function reportingConsoleError() {
  var args = Array.prototype.slice.call(arguments);
  Sentry.captureException(reduceConsoleArgs(args), { level: 'error' });
  return oldConsoleError.apply(console, args);
};

var oldConsoleWarn = console.warn;
console.warn = reportingConsoleWarn; // defined via function hoisting
function reportingConsoleWarn() {
  var args = Array.prototype.slice.call(arguments);
  Sentry.captureMessage(reduceConsoleArgs(args), { level: 'warning' });
  return oldConsoleWarn.apply(console, args);
}

function reduceConsoleArgs(args) {
  let errorMsg = args[0];
  // Make sure errorMsg is either an error or string.
  // It's therefore best to pass in new Error('msg') instead of just 'msg' since
  // that'll give you a stack trace leading up to the creation of that new Error
  // whereas if you just pass in a plain string 'msg', the stack trace will include
  // reportingConsoleError and reportingConsoleCall
  if (!(errorMsg instanceof Error)) {
    // stringify all args as a new Error (which creates a stack trace)
    errorMsg = new Error(
      args.reduce(function(accumulator, currentValue) {
        return accumulator.toString() + ' ' + currentValue.toString();
      }, '')
    );
  }
  return errorMsg;
}