A little more clarity: where you see “esri” in the lower right corner, the full image says “POWERED BY esri”. In other words, ESRI is the platform, not the publisher. It’s similar to use of Leaflet or OpenLayers for “powering” (providing the architecture to display) a rendering of OpenStreetMap tiles.
I’m not sure which editor you refer to as “the OSM editor”, but surely id has it, JOSM can specify it, and StreetComplete has numerous quests that are disabled by default for various reasons but can be enabled (with SCEE having even more).
As for routing priority, that depends on the routing profile used by the router; there are dozens of routing profiles among several routing providers, many of which probably don’t use smoothness but could. OsmAnd can — it targets some smoothness values like unpaved.
Possibly not “companion” per se, but Every Door is available for iOS and MapComplete can run in browser. Go Map!! can provide more detailed editing.
BRouter and other routing engines can use attributes like surface and smoothness (and probably width) to calculate routes.
Are you referring to smoothness=bad or a narrow width? (I’m guessing you’ve been using StreetComplete to specify each.)
Garmin has for a long time had live traffic data supplied by municipalities before smartphones became popular. But I’m not sure what you meant by “in-house” (surely not literal!).
Your area might be covered by opensupermaps.