I see that I've used the wrong category so you may want to move this thread to Membership Pro.
As you know we use an extended version of the API for our Shopify app. Shopify is enforcing Chrome's samesite cookie requirement. Even though we do not use any of the payment plugins for Shopify, the PHPSESSID cookie is present.
We use Paypal and Stripe for non-Shopify transactions. Another solution would be to eliminate the cookie entirely when not needed, but I suspect adding the attribute would be much simpler.