Cookie Optin box is shown even though cookie is set for cookie domain

We are using the setting set_cookie_for_domain (main domain) in backend. There are 3 another pages with a subdomain and all have the same cookie domain (main domain) set. If I set the cookie in frontend (cookieoptin opens and I confirm essential cookies) on the main page (with the main domain set in set_cookie_for_domain) then I expect that the cookieoptin window is not shown if I go to one of the other pages with a subdomain from that main domain. But this doesn't working. I have to check the cookieoptin stuff again. On every other page. The domain value in the cookie (set on those another pages) is correctly set to the main domain with a leading ..

You can test this live here: https://dgvn.de/

The subdomain pages are:

We are using sg-cookie-optin in version 4.2.9 on TYPO3 10.4.21

Issue occurs after an update from sg-cookie-optin version 3.2.8 and TYPO3 8.7. Before the update everything was working with the extra cookie domain set for all pages.

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