Hi neighbors. The Ring app on the Samsung Refrigerator is created by and maintained by the Samsung team. This is why it is visible on your IOS or Android devices, but not your Samsung Refrigerator. As a quick troubleshooting step, I would ensure that your Samsung Ring app is up to date, as the Ring Pro 2 is a new product and may not be visible on an older version of the Samsung Ring app.
If you are unable to resolve this with an update, I’ve located the Samsung Community here where you might be able to find a solution. Feel free to let us know how this goes.