It is impossible to tell which package belongs to which bulletin when looking at the Package Status By Package Server report as it shows duplicate package names. Take, for example, MSNS21-07-MRNET-5004333 (released on 7/29/2021) and MSNS21-08-MRNET-5004333 (released on 8/10/2021). You can see below that MSNS21-07-MRNET-5004333 lists the updates windows10.0-kb5004333-x64-ndp48-1909.msu and windows10.0-kb5004333-x64-ndp48-1909.msu:
MSNS21-08-MRNET-5004333 lists the updates windows10.0-kb5004333-v2-x64-ndp48-1909.msu and windows10.0-kb5004333-v2-x64-ndp48-1909.msu:
Notice in the screenshot above that the software update shows v2. When you want to make sure the downloaded updates are on your Site Servers, you may run the default report: Package Status By Package Server.
Notice that the report results shown in the screenshot below that you have no way to tell which package name belongs to which bulletin:
ITMS 8.x
Patch Management Solution 8.x
Unfortunately, Microsoft did not change the update names between the two bulletins. The default report pulls data from vRM_Package_Item. This view only contains the package name which does not show the v2 naming portion. So that is why you can't differentiate between the two.
This is working by design. The reports are working fine. Hopefully in the future Microsoft will name some of their updates differently so that you can tell which package name belongs to which bulletin.