The picture actually explains it but though I have not actually observe how fast the price always moves after halving, though if the graph is always accurate on the btc movement after halving, is going to be a big move breaking the all time high, is really good buying some amount of Bitcoin before it breaks the all time high.
Answer to your query is not fixed but a variable one because if we look at the history events of Halving, we will see not every bull run starts just after the halving, some took 6 months, some Tooks 3 months and one bull run Tooks 13 months, i think. The difference of months i told here is not confirmed but you could confirm them by searching on the google search engine by writing these prompts or in any AI tool which could provide you up to date data. "When did Bull run starts after halving of 2012, 2016, 2020" We can see halving took place in 2020 but ATH was set in 2021 which means the difference between these bulls run dates is huge and does not depend on each other.
But again I tell you, using Bitcoin to buy Heroine from the dark markets is actually one of its greatest use cases to illustrate censorship-resistance - the network's main value proposition. That it can't be shut down even if it's being used for "bad use cases" shows that it works.
But if BTC continues to be misused like this then authorities will take some bold actions against it but i think your intentions are just to show that BTC could be used for anything, and those authorities still cannot do anything at all and i am agree with you. 