Hi,
Support for Joomla 4 has been done a while back with HikaShop 4.4.0:
www.hikashop.com/home/blog/464-hikashop-4-4-0.html
I personnally use HikaShop on Joomla 4 (beta, then RC and now the final) PHP 8 since half a year on my main local development website and it works fine. We've also had several users already working on websites with the RC versions and HikaShop successfully in that time.
So no worries, HikaShop is compatible with Joomla 4.
I'm not sure how these upgrade checks are made. I suppose that they must check for code that isn't compatible with Joomla 4, like calls $app->isAdmin(). And we do have these here and there with a if on the Joomla version to do something else for Joomla 4.
Regarding the homepage, it's just that the text hasn't been updated yet there.
If you find other places where it is not updated do not hesitate to let us know.