button.addEventListener('click', function () {
document.querySelector('input[name="payment"]:checked');
inputCheckedRadio = document.querySelector('input[name="payment"]:checked');
if (!inputCheckedRadio) {
console.log('not checked');
return false;
}
});
<div id="step-3" class="order__form-step">
<p class="order__form-step-tittle"><span class="order__form-step-num">3</span> Оплата</p>
<div class="order__form-content">
<div class="order__form-item">
<p class="order__form-tittle">Способ оплати</p>
<label class="radio">
<input required name="payment" type="radio" class="radio__input js-input-radio">
<span class="radio__fake"></span>
<span class="radio__text">Наличными при получении</span>
</label>
<label class="radio">
<input name="payment" type="radio" class="radio__input js-input-radio">
<span class="radio__fake"></span>
<span class="radio__text">Оплатить картой сейчас</span>
</label>
<label class="radio">
<input name="payment" type="radio" class="radio__input js-input-radio">
<span class="radio__fake"></span>
<span class="radio__text">PrivatPay</span>
</label>
<label class="radio">
<input name="payment" type="radio" class="radio__input js-input-radio">
<span class="radio__fake"></span>
<span class="radio__text">Расчетный счет</span>
</label>
</div>
</div>
<input type="button" value="К предыдущему шагу" class="order__form-btn prev-button">
</div>