localStorage is not shared between tabs

Steps to reproduce:

1. open some web site
2. open the same page in another tab
3. open Web Console in both tabs
4. set localStorage['test']=1 in the first tab
5. try to get the value of localStorage['test'] in the second tab.

Result: The value is undefined.

Expected result: The value is 1.

Tor Browser 9.0.1. Tested on onion sites with enabled js.

Please, please fix this, it is very important, I've developed an app that relies on this functionality and I didn't expect that there will such problems with localStorage. Please don't tell me that this behavior is intentional. It shouldn't be for the same origin.

Trac:
Username: nDe15o