Welcome too the Serif Affinity forums.
There are two kinds of brushes, raster and vector.
If the brushes are raster they will appear in Photo, in the Photo Persona of Publisher, and in the Pixel Persona of Designer once they're installed.
If they're vector they will only appear in the Designer Persona of Designer, it the Designer Persona of Publisher.
So probably nothing is wrong, except which application you're using or which Persona of that application you're using.
OlgaK got a reaction from walt.farrell in Purchasing brush don’t visible in the brush list