The U-Turn on Indiana Toll Road is an interesting one! It looks like Organic Maps' router is making use of a road that's tagged as an emergency service road in OSM:
The road was added three months - apparently based on "updated satellite imagery" - but poorly tagged. It was then edited 9 days ago to improve the tagging.
OSM updates instantly; every edit is an immediate operation on its database. Tile refresh on the official website (which is little more than a tech demo) may take a little while, though it could be you just need to refresh your browser cache. The OSMAnd app updates map data once a month, unless you enable OSMAnd Live where map updates come hourly.
https://www.openstreetmap.org/way/1186446719
The road was added three months - apparently based on "updated satellite imagery" - but poorly tagged. It was then edited 9 days ago to improve the tagging.
https://www.openstreetmap.org/way/1186446719/history
Perhaps the more recent edit was from Organic Maps so that their router handles the tags appropriately?
Looking at this area on Google streetview (from June 2023), I can't see anything that looks like a service road:
https://www.google.com/maps/@41.5920007,-87.2303049,3a,90y,3...
I wonder why Organic Maps would take the U-turn rather than the more obvious ramp. Perhaps it is to avoid the toll gate?
Also, regarding this:
> it can take a few weeks for an OpenStreetMap update to get pushed out
OpenStreetMap updates within a day or two, but Organic Maps' own ingest process might have a lower frequency.