I can't decide on a class for him that would suit him best and be convenient to use. Firt i was dual wield dex Oathbreaker, but after multiclass and renewing the oath for ability respec i had a bug, second try was barbarian and i missed mostly of time even with reckless attack with 75-80% chance. What should I try for him? At the moment i look at something assasin-like due to his biography and past, but can't decide which class to pic and multiclass, i like shadowmonk, gloom stalker and assasin but i don't know which of them are available for multiclassing and will be good ad building, also i look on oathbreaker paladin but STR based and don't have plans of respec him, but can't decide which multiclass should i take. Also Warlock is good option but is it really work to do something like assasin warlock?
The way I see it there are 5 "roles" in an efficient 4 player group. A character/player can have more than 1 role.
Rogue Type (Monk, Bard, Rogue, Ranger)
Control/Healer (Cleric, Druid, Bard)
AOE DPS/Lore/Arcana (Wizard, Sorcerer, Bard, Warlock)
Tank DPS/Heavy, STR build - (Barbarian, Fighter, Ranger, Paladin)
Face Character - (Sorcerer, Paladin, Bard, Warlock, Rogue)
Bard is not good because it's amazing on the battlefield as far as damage done, but because they can fill SO many roles needed.
Now the classes you mentioned.
1. Gloomstalker - doesn't quite fit him since he is a city boy. Strong build, does lots of damage though.
2. Assassin would make sense for him of course, but honestly the assassin subclass is pretty terrible. There is really only 1 good rogue subclass - Thief. Frankly I would ditch the subclass and make a Fighter/Thief, as that would fit and he would be very strong on the battlefield and in a martial sense. Barbarian doesn't really fit the "cold methodical killer" mentality. Ranger doesn't fit his City background.
3. Shadow Monk - Frankly I love this build and the idea of this, as well as multiclassing it with Fighter- insanely strong/yet subdued. Nothing in bg3 kills as fast as a Monk, and having that ability to move through shadows and kill with your hands feels very dark urge. Assassin would also work here because the Monk side is so strong, but of course Thief is much better.
4. Assassin/Warlock isn't terrible but it also creates a strange conflict with you needing a patron but also being a Dark urge? I don't see it working really canonically. Although Pact Weapon/Assassin may be fairly strong.
I'd go with the Shadowmonk build and throw fighter in there.