Takes about three weeks for it to work.
i dont know where three weeks comes from.
but i do agree with you, that it does seem to be working in a kind of gradual process.
yesterday it slowed down the pace of its charging when it got to around 76% and it really was unusually slow at the pace of advancing after that.
so it is working, and it is taking time, as you mention.
in my case, i can also add that i keep very dramatically changing hours of intensive use / waking / charging / daily different wake alarms, etc.
so if there is no regular schedule for it to follow, it would be clear it cant figure out an established pattern and therefore delay a kind of charging pattern.
i can also add that in fact, battery life on my iPhone 6s has been slowly inching up better day by day.
especially in keeping/holding a relatively higher charged state longer and not dramatically reducing battery charge just through background / maintenance functions.
when iOS 13 initially came out, my iPhone 6s would lose about 25% overnight.
last night it lost about 5%.