

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.
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.