Me neither and thanks a lot for pointing this out @coagmano @copleykj and it certainly is going to be something I will remember and use!
Yet, I still think localStorage is for “storing” information in the browser as the name impliies whereas the op is looking for a solution to send information from one tab/window to another, for which, the intended - and aptly named - api is postMessage.
Also, localStorage has storage limits that might require cleanup during long sessions of data transmission or simpli might not be able to transmit large chunks of data due to said limit. Incognito mode also adds more complexity to the behavior as it is not described in the spec and is implemented differently by vendors.
Furthermore, we have not yet even asked questions about the nature of the data to be transmitted. Is it sensitive? Is it okay to store and keep it on that device?
As for the reactivity of the data to allow propagating it to to the whole ui on the target window, yes a ReactiveDict (Session) sounds like a good approach to cary over and implement a global, reactive ui state store, especially (not necessarily exclusively, though) for a Blaze app.