Generating random points inside polygons that capture values from multiple attribute fields

I have some census block data where one attribute field is a total count (let’s say number of homes), and then additional attribute fields disaggregate counts in different categories (e.g. home value might have 5 bins: 50k-100k, 100k-150k, etc…). I’d like to create a shp file in QGIS that generates random points for each home in each block polygon but also retains the attribute name of the disaggregated counts as a value in a new attribute field. EG, each point would have a new categorical attribute called “home_value” with a value like 50-100k or 100k-150k.

I think I could do this by generating a different layer for each attribute using “random points inside polygons (variable)” and then merging the layers, but I’m hoping there is some easier way.