As the BPost API is quite peculiar compared to other shipping services, we've have to develop the BPost shipping plugin in a one that is closely linked to the old checkout of HikaShop, from before HikaShop 3's new checkout.
So it doesn't suprises me that the plugin has issues with the new checkout of HikaShop.
Unfortunately, to be able to make it work with HikaShop 3's new checkout will require more than a small patch here and there but some redevelopment, with proper testing etc.
First, this will take some time, and it will also require having test credentials in order to be able to do the testing.
The testing credentials had been provided before by the Joomla project as we developed that plugin first for them. However, we can't use them anymore.
Would you be able to provide the necessary test credentials for us to be able to work on that ?
In the mean time, I can only recommend using the legacy checkout if you need to use the BPost shipping plugin.