I found the paper which probably has the answer

http://wiki.squeak.org/squeak/5822

On 5/12/18, H. Hirzel <hannes.hirzel at gmail.com> wrote:
> Hello Bert
>
> I wonder if and how it is possible to get/store values of the
> localStorage of the browser.
>
> Or are there other mechanisms to save state between subsequent calls
> to work with a Squeak image file in the browser?
>
> Regards
>
> Hannes
>