Hi! I'm no expert, but have experimented with this sort of thing. As far as I know:
OsmAnd's elevation data comes from the NASA SRTM/ASTER data that is available freely for the whole world except towards the poles. This has a horizontal resolution of 1 arc-second, about 30 metres. The vertical accuracy varies but seems to be no better than +/-5m. So it doesn't make sense to have contour line spacing too close.
OsmAnd's contour lines are pre-computed in the download, rather than being generated dynamically on your device from raw elevation data, so you can't try closer spacing just by tweaking the rendering styles.
Many countries are providing open access to more accurate DTM/DEM data from LIDAR surveys. In the UK we have this only for flood modelling, which if one's interested in hills is the opposite of what one wants! LIDAR data can be amazingly accurate, e.g. you can see the shape of a car. If you have such data, you can generate your own contour lines in QGIS and get them to show in OsmAnd. If you're interested I could post some notes I made when I tried it, but it requires a little dedication. I found that I could now see features such as cliffs and quarries that had not been marked as such on OSM, but for me it wasn't worth the large file sizes of what I had generated. That was three years ago when OsmAnd's minimum spacing was 10m - I hadn't noticed that the "high" setting now gives 5m. This shows my missing quarries, but must be the limit for SRTM data. (Unless OsmAnd is now tapping in to LIDAR? I can't find any information on that.)
Just google any of the terms I used if you're not familiar! I hope that's of interest.