Before the story begins, there’s a few things that are worth knowing:
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There exists an organisation called Providence. They are basically the Illuminati and their members are highly wealthy and influential. This allows them to effectively run the entire world behind the scenes. They are also the group that funded Ort-Meyers cloning project, which is what created 47.
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The structure of Providence is this: There are all the regular members, they will provide information to “Heralds” which is basically the middle man, one of the heralds is actually being interrogated in Colorado, The Heralds pass the information on to “The Constant”. This is the same guy you kidnap off of the Isle of Sgail. The Constant is the only person in the world who knows the identities of the three partners. These are the people at the very top of the organisation. The Constant confers with them when making decisions
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47 is not the only clone to have survived all this time, Lucas Grey (Subject 6) is very much alive, and unlike 47, he has a full conscience and range of emotions. In the comic series, 47 and Grey attempted to escape the asylum they were raised in, but 47 sacrificed his own freedom to allow Lucas Grey to escape. 47’s memory is then completely wiped. To be extra sure, they tell 47 that Grey had died during the escape.
Pictures for Reference
Lucas Grey
The Constant
The Partners
Before the beginning of Paris, Lucas Grey has been able to learn much more about Providence. He begins a war of revenge, determined to crush the organisation. Part of his plan is to manipulate the ICA to perform contracts that would benefit him in his goal. He anonymously gives hints and tips to businesses and individuals, who will then use the ICA to perform assassinations for them, unknowingly helping Lucas Grey.
In Paris, Sapienza and Marrakesh, all your targets are providence members or assosicates, and their elimination is just a part of the war
Bangkok is a little different, Lucas Grey planned to rob reclusive billionaire Thomas Cross, but he has not left his private island in years. He manipulated another client to place a contract on his son Jordan Cross. He planned to intercept Thomas Cross at his sons funeral. His plan worked, and he managed to loot over $3 Billion from his accounts to be used in his war.
After Thomas Cross’ murder, the ICA finally put together the pieces. ICA are truly neutral and do not take sides in any conflict. For this reason, the ICA board of directors order 47 and Diana to hunt down the “Shadow Client”, Lucas Grey.
The ICA are able to track the Shadow Client to a farm in Colorado. The militia you see in the map are all under the command of Lucas Grey. 47 takes out 4 key targets to try and cripple the militia’s command. In the Tornado Shelter, 47 finds all of Lucas Grey’s research. This proves to him and Diana that providence, a hypothetical concept, does in fact exist. They also discover that Erich Soders, a senior member of the ICA, is a providence operative. ICA has been compromised.
The rest of the ICA is appalled by this discovery, and immediately order 47 to kill Soders and a providence lawyer in Hokkado.
After the mission, the constant approaches Diana on a train and makes an offer: Providence and the ICA have a common enemy, they should work together. If they do, the Constant offers the true origins of Agent 47.
The ICA executives decide to accept his offer. From this point, they will be offering contracts that target Lucas Grey and his militia.
Hawkes Bay, Miami, Colombia and Mumbai are similar to the first 4 missions in season 1, they are almost unrelated and are simply targeted strikes against the militia.
During this time, Lucas Grey acquires the antidote to 47’s memory wipe, and leads a trail to the asylum in Romania. When they meet, Grey proves that he and 47 are brothers, 47 can even remember his name, proving some fragments of memory survived. 47 willingly took the antidote. He remembered the providence representative who came to the asylum. It was he and Lucas Grey’s mission to destroy providence years ago due to the torture the were put through
That representative was Janus, the former providence Constant. They hatch a plan to set him up as the real shadow client who was working behind the scenes. They will assassinate him, and search for information about Providence (the clues)
Janus was the original founder of the Ark Society, the group you see on Sgail. They have a plan to track Janus’ coffin, as the Ark Society will likely want to hold a private funeral somewhere. The plan is successful.
In Whittleton Creek, they confirm that the current Constant will be at the meeting of The Ark Society. The original plan is to simply kidnap him, but they soon learn that the Constant has a poison chip in his neck, a final failsafe. The two kill switches that will detonate the device are with the Chairwomen of the society, making them necessary targets.
The mission succeeds, and the Constant offers up the names of the 3 partners. The partners have prepared for this scenario, however, and are currently faking their deaths to minimise their chance of death.
There is a lead to be followed, the partners use the Bank in New York frequently. Everything has happened so recently that the bank records are still unchanged, and are the only lead on the new identities of the partners. 47 has to kill Athena Savalas for no reason other than the mission needs a target 
The bank accounts lead to Haven Island, a service that helps people to vanish from the world with a new identity. The partner’s current identity and location are on their servers, but the 3 owners manually reset the servers every 10 hours. 47 is forced to eliminate the owners so the servers can be hacked.
After the mission, 47 and Lucas know where the partners are. But a confusing series of events happens next that is left pretty vague. The Constant escapes his captivity, and all of the partner’s power and wealth is sent to him. Its hard to say for certain where this will head.
All we know now is that the partners are targets across Dubai and Dartmoor.
tldr
Lucas makes ICA kill Illuminati dudes, Illuminati makes ICA kill Lucas’ guys. 47 and Lucas dream team and kill Illuminati leaders
If I recall correctly, Both Viktor and Dalia have no affiliation to Providence. IAGO is simply a way for Lucas to gain information on Providence by doing a kill for Viktor. The rest of the targets you’ve mentioned are all Providence members indeed.
T’is the result of replaying Hitman cutscene to cutscene last month to prepare for Hitman 3, haha.