The Stripe public docs have a pretty good walkthrough that describes the recommended way to handle this:

https://docs.stripe.com/billing/subscriptions/build-subscriptions?platform=web&ui=elements&lang=java#create-subscription

In short, the flow is:

• Your backend creates subscription and uses expansion to pass latest_invoice.payment_intent.client_secret back to frontend.
  • The payment_settings.save_default_payment_method parameter can be used to tell Stripe to automatically save the payment method later on.
    https://docs.stripe.com/api/subscriptions/create#create_subscription-payment_settings-save_default_payment_method
• Your frontend mounts the payment element using the client secret you get from your backend.
• When the frontend Stripe payments element is submitted, you use stripe.confirmPayment to confirm payment details immediately and try to charge the card. This is also where Stripe will automatically save the payment method, assuming you passed the correct params in step 1.

Here’s the relevant code snippet that shows you how you should configure your server code to save the default payment method and pass the client secret back.

// Set your secret key. Remember to switch to your live secret key in production.
// See your keys here: https://dashboard.stripe.com/apikeys
Stripe.apiKey = "your_test_key";

post(
  "/create-subscription",
  (request, response) -> {
    response.type("application/json");
    String customerId = request.cookie("customer");
    CreateSubscriptionRequest postBody = gson.fromJson(
      request.body(),
      CreateSubscriptionRequest.class
    );
    String priceId = postBody.getPriceId();

    // Automatically save the payment method to the subscription
    // when the first payment is successful
    SubscriptionCreateParams.PaymentSettings paymentSettings =
      SubscriptionCreateParams.PaymentSettings
        .builder()
        .setSaveDefaultPaymentMethod(SaveDefaultPaymentMethod.ON_SUBSCRIPTION)
        .build();

    // Create the subscription. Note we're expanding the Subscription's
    // latest invoice and that invoice's payment_intent
    // so we can pass it to the front end to confirm the payment
    SubscriptionCreateParams subCreateParams = SubscriptionCreateParams
      .builder()
      .setCustomer(customerId)
      .addItem(
        SubscriptionCreateParams
          .Item.builder()
          .setPrice(priceId)
          .build()
      )
      .setPaymentSettings(paymentSettings)
      .setPaymentBehavior(SubscriptionCreateParams.PaymentBehavior.DEFAULT_INCOMPLETE)
      .addAllExpand(Arrays.asList("latest_invoice.payment_intent"))
      .build();

    Subscription subscription = Subscription.create(subCreateParams);

    Map<String, Object> responseData = new HashMap<>();
    responseData.put("subscriptionId", subscription.getId());
    responseData.put("clientSecret", subscription.getLatestInvoiceObject().getPaymentIntentObject().getClientSecret());
    return StripeObject.PRETTY_PRINT_GSON.toJson(responseData);
  }
);