Why is the client_secret missing when using billing_cycle_anchor_config for Stripe subscriptions in PHP?

I'm setting up a Stripe subscription in PHP and run into an issue: when I include billing_cycle_anchor_config to schedule the subscription for the 15th of every month, Stripe doesn't return a client secret. Without billing_cycle_anchor or billing_cycle_anchor_config, Stripe returns a client secret for the PaymentIntent, which I need to initialize stripe.elements({clientSecret}) in JavaScript and show the payment form.

I have a monthly price (greater than zero) for the product/price (price_1QdcAbQ2RrzncYBtx2HyrHYj), and the customer is valid. I use the following PHP code with billing_cycle_anchor_config to set the subscription processing day:

PHPCopied
<?php
$subscriptionConfig = [
    "customer" => "cus_RWSKEbtu8uiIaj",
    "items" => [
        [
            "price" => "price_1QdcAbQ2RrzncYBtx2HyrHYj"
        ],
    ],
    "metadata" => [
        "user_id" => 1,
        "donation_type" => "recurring",
        "recurring_day" => "15",
    ],
    "payment_behavior" => "default_incomplete",
    "expand" => [
        "latest_invoice.payment_intent",
    ],
    "billing_cycle_anchor_config" => [
        "day_of_month" => 15,
    ],
    "proration_behavior" => "none",
];

$subscription = \Stripe\Subscription::create( $subscriptionConfig );

// I must have a client secret, or I cannot show the payment form to the customer
$clientSecret = $subscription->latest_invoice->payment_intent->client_secret ?? NULL;

I need to let the customer choose the processing day for their subscription, but now there's no immediate PaymentIntent (and thus no client secret). What am I doing wrong, or is this the expected Stripe behavior when scheduling future invoices?