I am implementing Payment Links for recurring payments on my website. Stripe automatically handles customer creation and subscription management when a customer pays using a payment link. However, I am facing an issue where duplicate customers are created ( same email ) if the same customer pays multiple times using payment links.
Depending on how you're wanting to handle subscriptions, there is a feature where you can limit your customer to have one Subscription. It uses their Customer Portal for your customers to manage subscriptions and upgrade or downgrade in their UI. The intended use for their Payment Links is for you to be able to share the one link as many times as you want so there is a not an option to pass in a customer ID so a customer will be created every time they use a Payment Link in subscription mode.
However, if you'd like to offer your customers the ability to have multiple subscriptions, then you'd want to use their Stripe Checkout product. This allows you to either embed or use their hosted page to collect payments and pass the customer ID that is already created so they can have multiple subscription on that customer ID.