You’re right:
It don’t work in: Chrome, Opera
It worked in: Safari, Firefox
In Chrome, the cookie is not set
In Firefox, the cookie is available:
But Chrome is my standard-browser - the latest version 115.
I had no issues with cookies in other applications.
I have no addon installed and the private settings allow all cookies.
The Local storage contains the ghost-history. The Session storage is empty. The same as in Firefox.