Inteagrate external website with SSo and few mail issues to be sorted out

An external website needs to be integrated with woo - commerce for payment gateway purpose. Both the external website and woo - commerce are prepared and ready. Only few things are left, which I expect to be done in a day or 2: 1) Create SSO (maybe using wordpress JWT) for woocommerce so that when user logs in the external site, the users gets automatically logged in to woocommerce, to access payment gateway. 2) Also, ensuring that any update in user info in external website automatically gets updated in woocommerce via API. 3) Switch to SMTP instead of WordPress default mail function to avoid mail bouncing. 4) A few mail related issues (pretty small ones) need to be sorted out. 5) Update sitemap and update it in google search console. Note: the external website server is not accessible Expect guys who have past experience in woocommerce/wordpress api to apply, as I have time constraint.