Well, it can show traffic data as overlay via Raster maps using the Online maps plugin, but not consider it automatically in navigation.

Here are various traffic layers of proprietary providers that can be added as online map source: https://anygis.ru/Web/Html/Download_en?shortSet=true&app=OsmandSqlite

CoMaps is working on integrating traffic data as well (see also related issue), which is currently considered as “App Priorities”. So keep an eye on it.

NUNAV by graphmasters.net. It’s more minimalistic (only one route suggestion, no offline maps), but also based on OpenStreetMap + traffic data. I still have to test it but seems a promising alternative.