I just tested again and the issue is still there.
1) I opened my website on desktop and connected to my account
2) I opened my website on mobile and connected to my same account
3) I added a product to compare on mobile
4) I refrshed the same compare page on desktop
AS IS :
The product added to compare on mobile does not show on the compare page refreshed on desktop. And vice versa.
TO BE :
The product added to compare on mobile should also show on the same page refreshed on desktop. And vice versa.
COMMENTS :
1) The compare feature should be linked to the account. If a user naviguates on a website through different devices, then his data should be retained over the different devices.
2) That’s why I think good to think about adding the compare page in the account section of WooCommerce (just like the favorites page added by YITH in that account section)