Hello apple_mac_user_01,
Let’s see how we can help out today with your Apple Watch and Safari today.
Is your Apple Watch updated to the latest watchOS 8.1? Update your Apple Watch
Have you visited this site before on your Apple Watch? If so, did you have the same behavior, the app closed?
Do you have this issue with any other websites when using Safari on your Apple Watch?
Let us know more details so we can look into this with you.
Look forward to hearing back from you!