I am tempted to visually look for logical groupings of houses (city block, similar looking houses/apartments, etc), and create “landuse=residental” areas for them. However, some of them are already encapsulated in neighborhood areas like https://www.openstreetmap.org/way/999224230#map=16/40.4058/-86.8706 .
I’m not sure if there is any well-defined approach to mapping residential landuse. Some map large areas of towns and cities with a single polygon, others carefully map to exclude the highways and sidewalks. Personally, I think the latter is perhaps over detailed.
When I started we didnt have detailed aerial imagery in many places so landuse=residential was a big help to delineate towns and villages when there was no road network. This approach is still commonly used in mapping in the developing world as one can quickly identify where additional mapping is needed.
In your case I would probably use major roads, possibly down to tertiary to delineate blocks of residential usage, pretty much as you have done for neighbourhoods. In the first instance you could just add residential=landuse to the neighbourhood polygons, but this gets messy as soon as you want to split something out into another landuse, or just exclude it from residential. For instance the school and the big church opposite the baseball park might belong in the neighbourhood, but not be residential. So probably create another polygon for now sharing the same nodes for the residential areas & these can then be refined (reduced in size) as you map more detail.
If there are named areas which don’t fit neatly into the place=* hierarchy then having a specific named landuse=residential for that area can get round working out exactly what kind of place it might be (examples from my own mapping: blocks containing social housing; large-scale purpose-built student accommodation (PBSA); named areas of sheltered housing for the elderly, historical areas subsumed in larger neighbourhoods)
At this scale it is extremely useful to find any groups of shops and tag those with a separate landuse=retail polygon (again provides some information about the structure of neighbourhoods even if the shops aren’t mapped themselves). For instance there seems to be a small commercial/retail grouping at the Kossuth/16th junction. Purists will insist the landuses do not overlap, but in practice , and as demonstrated by the main OSM map, this is not strictly necessary.