This idea comes from a question asked on the community:
The community member would like to see Session Storage added as a Data Element option in addition to Local Storage.
The product team is aware of this request. It is logged under DTM-10315.
This is now available in Launch:
I'm a little late to the conversation, but I wanted to chime in to add that the SDI Toolkit extension provides Launch Actions for setting and removing sessionStorage and localStorage values.