overleaf/services/web/frontend/js/features/form-helpers/captcha.js

const grecaptcha = window.grecaptcha

let recaptchaId
const recaptchaCallbacks = []

export async function validateCaptchaV2() {
  if (typeof grecaptcha === 'undefined') {
    return
  }
  if (recaptchaId === undefined) {
    const el = document.getElementById('recaptcha')
    recaptchaId = grecaptcha.render(el, {
      callback: token => {
        recaptchaCallbacks.splice(0).forEach(cb => cb(token))
        grecaptcha.reset(recaptchaId)
      },
    })
  }
  return await new Promise(resolve => {
    recaptchaCallbacks.push(resolve)
    grecaptcha.execute(recaptchaId)
  })
}