Hey there! Please note that place=district is a specific administrative division in some countries: https://wiki.openstreetmap.org/wiki/Tag:place=district?uselang=en. The tag is basically unused in the US: https://taginfo.geofabrik.de/north-america:us/tags/place=district#overview.

place= tagging is a little counterintuitive to Americans since the names come from British English: the urban hierarchy within cities goes 'suburb' > 'quarter' > 'neighbourhood' (see https://wiki.openstreetmap.org/wiki/Key:place#Populated_settlements,_urban). So since place=neighbourhood is the smallest possible urban place, it's OK for it to be within, say, Capitol Hill (a place=suburb https://www.openstreetmap.org/node/158502198). Neighborhoods also don't have to be official to be mapped, they just have to be a name for an area known to locals. So I would be in favor of switching Lincoln Park back to place=neighbourhood.

Happy mapping!
Will