How the fuck was their insidious group not hunted and utterly destroyed by the global community after WW1 concluded?
That’s like if Hitler and his right hand men managed to escape from the consequences of WW2.
It seems that you are assuming that the Black Hand was the actual cause of WW1. While the assassination of Franz Ferdinand was the trigger that set in motion the events of WW1. The entirety of Europe was 1 big powder keg and war was basically inevitable.
You have to imagine that Nationalism was a fairly new concept for Europe which had only gripped the continent the pas century and around this time everybody was proud to be part of their country. Or they wanted their own country for their own nation.
Franco-German relations were at an all-time low, especially after the Franco-German war which ended with the Prussian king being crowned Emperor of Germany in the Palace of Versailles. Imagine being defeated in a war and your enemy proclaiming himself emperor in YOUR palace. So they were gunning for a fight.
While France and Germany stem from relatively the same groups going way back to the tribes that settled in those areas around the fall of the Roman empire, and their respective proto-nations more or less being formed with the split of the Frankish Empire (with the grandsons of Charlemagne). Thus they found their nationalism in their shared heritage.
Austria was experiencing massive internal struggles due to this aforementioned nationalism. Austria itself was semi-part of the HRE and due to some political difficulies declined being part of the German Confederation. Then it was in a wierd semi-personal union with Hungary which merged into an Empire and they conquered lands in the Balkans. Thus leading to 1 country with many different heritages, languages, cultures and subsequently nationalisms. This caused groups like the Black Hand to struggle for independence (in their case Serbia). Serbia was semi-autonomous at the time (I don't know exactly Austria-Hungary had a very complicated structure)
And across the continent this nationalism either caused internal struggle or external due to the perceived need to show the power of your country and maybe you felt like 1 area should belong to your country (e.g. Alsace-Lorraine).
This led to ever increasing inevitability of war and even the want for a war. If you see film from the start of the war and the soldier departing they are happy and proud to go. They wanted to show that their country could defeat the enemy.
The other major factor was alliances. There was a complex network of alliances between different countries and groups. Russia was allied with Serbia and France. Austria was allied with Germany. Belgium was allied with the UK etc. etc.
These alliances led to the escalation of the war to a world war because when Austria demanded repremands from Serbia for the death of Franz Ferdinand. Serbia didn't want or couldn't give those. Austria retaliated and this led to Russia declaring war on Austria. Then Germany declaired war on Russia and in turn France declaired war on Germany.
Germany looking for a fight with France anyway went to.full scale war, but in order to bypass French defensive lines they decided to just go through Belgium instead. This led to the UK declairing war on Germany because the UK was the protector of Belgium ever since the 1839 conference of London.
At the same time due to their mother nations going to war, their colonial states also went to war and seeing there weren't many independent states at the time the term World War is quite literal in this sense.
But historians agree that even if Franz Ferdinand had not been killed something else would have caused the war maybe a few years later. But was would have come anyway. Would the war have gone differently? Maybe but personally I am not the biggest fan of "what if? History"
Tl;dr Franz Ferdinand's assassination was only the spark that lit the powder keg. Europe was filled with tention and war was as good as inevitable.