Your question is not related to SameSite.

First, if SameSite=None is set, the following becomes possible:

You are originally logged in at webshopA, and the cookie has SameSite=None specified.

Next, you navigate to webshopB, and from a page on webshopB, you navigate to a page on webshopA using the POST method.

In this case, the cookie with SameSite=None is sent to webshopA.

If this cookie has SameSite=Lax, it will not be sent to webshopA with the POST method. If it's the GET method, it will be sent to webshopA.

SameSite=None does not cause cookies to be sent to other sites. It changes the behavior when navigating from other sites.