Originally reported in 4606-gh-woocommerce/woocommerce-subscriptions
Similar issue to Automattic/woocommerce-payments#8029

Describe the bug

When attempting to purchase multiple subscriptions of varying periods with Apple/Google Pay, you will get an "Invalid recurring shipping method." error:

After some initial investigation, I believe this issue is caused by Stripe's payment request handler unintentionally wiping the recurring shipping methods from the chosen_shipping_methods session when it calls WC()->shipping->reset_shipping(), which is called when calculating the shipping options to display in the Apple/Google Pay pop-ups.

Before we wipe/clear the chosen shipping methods, we store them in a variable here so I think to fix this we'll need to restore any other chosen shipping methods that were wiped.

Additional details

Example of shipping_method data from payment button $_POST:

Array
(
    [0] => free_shipping:2
)

Example from a default checkout process:

Array
(
    [0] => free_shipping:2
    [2024_04_12_every_3rd_month_0] => free_shipping:2
    [2024_03_12_every_2nd_month_0] => free_shipping:2
)

To Reproduce
Steps to reproduce the behavior:

1. Install and activate the latest Woo Subscriptions plugin
2. Enable/activate Apple Pay and Google Pay payment request buttons
3. Create two subscription products with different billing periods (monthly and weekly)
4. Add both subscription products to your cart and navigate to the checkout page
5. Purchase the checkout with Google Pay
6. Notice the error seen in the screenshot above

Expected behavior
A clear and concise description of what you expected to happen.

Screenshots
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Environment (please complete the following information):

• WordPress Version
• WooCommerce Version
• Stripe Plugin Version
• Browser [e.g. chrome, safari] and Version
• Any other plugins installed

Additional context
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