Why is it that after I updated Halion 7.5, half of the instruments won't load? Has anyone else encountered this problem?
Yes, other users ran into the same problem, too. You will find numerous recent threads on this topic and possible solutions in this forum where everything has already been explained in detail. Please, use the forum’s search engine.
Nothing to worry about 
Speaking for the pedants among us, the image is of HALION SONIC, not HALion.
Can we assume you actually have licences?
You could check out this thread as a first stop …
Well, that is the underlying issue. The problem is that the “Install Missing VST Sounds” update in Download Assistant ended up installing a bunch of stuff we don’t have licenses for, and you have to manually remove those packages in Library Manager to remove the unlicensed packages. Here’s a link to one of the threads @Reco29 was alluding to above that discusses this (and it includes a link to another thread that has even more detail):