I went through solution which Lukas told me about (instead of retrieving variable from local storage), and, of course, it was successful. Solution was very easy: I just created new non persistable entity and everything was solved. :)
Lukas, thank you very much for instructions.
Nanoflows are run locally on client, so this might be an alternative, however still, you need to read the local storage through a widget.
There is a widget that you can use for reading and writing to local storage: https://appstore.home.mendix.com/link/app/52055/.
Perhaps this helps.
Your request seems a bit un-mendix to me. Can't you create a non persistent entity that is associated to the session entity instead of writing and reading the local storage? The HTML snippet does provide an optional on-click microflow event that might help you out here.