When I use osmAnd on my iPhone, the first time it needs to make a GPS fix, no problem.
But when I walk for 5 minutes, and then open the iPhone and check the map again, osmAnd first shows the location where it was last time, then after some seconds jumps to another location, then seems to need to make an new fix, which can take up to 30 seconds. Anyway, osmAnd does not follow my location in the background.
I am on an iPhone 8 with iOS 13. osmAnd has "Always" location access.
I had the same problem on my earlier iPhone SE with iOS 11.
But on Android, I did not see this problem: after an initial fix, the location would be stable and follow my walk in the background.