Currently, there is no built in way to share a cart with the Storefront API. This is a feature we have considered so I will make sure the team is aware you are requesting this.
we’ve recently bump into the same problem. We found a way to share the cart, by saving the checkout id in our back-end and retrieving it from there, then calling the ios/android/webjs sdk to get the checkout node. It looks like everything is working so far, with one single problem: We have to use the same storefront api key (shopify app) for all platforms, otherwise the checkout cannot be retrieved.
However, this could lead us to another problem since the transactions reporting in analytics might show everything coming from the same source.
Is there any way we can use the same api key, but still segregate the analytics reports?