Since you're busy, I'll apply a few gap fillers too and some detail. TS called SY 'my puppy' when he's in bed with him but it's a term of endearment this time. You can probably guess from the expressions at the start but TS immediately regrets choking out SY and asks if he's okay.
With the flashback and the past, SY doesn't bring his mother back home because he sees she's enjoying her life, and there's no way he could ever bring her back to her father. He regrets that he was weak and he wasn't able to protect her, and regrets that he couldn't do anything. So he told himself that he would become strong.
TS says he's not hiding anything about the past, but it's been confirmed that the first person that TS ever killed was SY's father, so he's definitely hiding something and afraid SY will react badly if finding out (I mean it is kinda bad). SY does admit that his father is trash though, so perhaps the reaction may not be as bad as TS thinks, but the hiding from SY will likely hurt him more. That being said, although SY was taken care of sometimes by his uncle, it's been shown and implied that his uncle was also kinda trash, so it's not like he was superb either.
In the conversation with Yawon she confirms that Kangil is still alive. The three triads were fighting for power and originaly one of them was Kangil's leader, but TS broke the balance between them. Zhou Yu Long has entered Korea after realising that there is a power struggle between the triads. Yawon says that she isn't on anyone's side at the moment, because she doesn't know who's going to win the power struggle war, but since she's friends with TS personally, she will give him information about Zhou Yu Long. Which ends up being in the form of a photo to SC with Zhou Yu Long and Jisung (presumably).
There's also speculation that the scribbled signature from the previous chapter for who visited SY's uncle's grave is actually Jisung. It's implied that Jisung has gone to Zhou Yu Long to get revenge on TS.
Hope this helps fill in some gaps for you, articxs.
Thank you for the details! I'm excited to see more gang action picking up and jisung returning to the picture as one of the main villains.
Short summary because I had a very stressful day at work today and don't have the brain power to explain all the scenes in detail. Sorryyy ┗( T﹏T )┛
After Sooyoung cums from being choked he admits to Taeseung that he was at his office and and saw TS laughing/smiling at someone and that's why he was annoyed. TS asks if SY came because he missed him and SY admits that yes, he did miss TS. Once they're in bed TS tells SY that the woman he saw was just a friend, and then asks if SY is hurt and SY says no, he's been through worse. And then that prompts a conversation about SY's past and his relationship with his uncle. It turns out his father is an abusive piece of shit and would ask SY to go bring his mother back or else he'll kill him. Turns out his mother is enjoying her own life with her own family and SY sits outside thinking that his father is gonna kill him since he can't bring his mother back home. His uncle ends up being the one to take care of him and that's why SY was at his grave site to see him.
Back in bed SY thinks about how lonely he was back then, and how he has someone in his arms now. SY asks TS to talk about himself and his past, and TS deflects saying it's nothing interesting. SY says he won't force TS to talk about it as long as he's not hiding any secrets (BUT HE IS!!). TS tells him to go to sleep and kisses him goodnight.
In this next scene Yawon outlines to Sangcheol about how there are 3 competing factions in this territory (The mayor who was introduced in ch 41 and his gang connections, Taeseung and his crew, and Zu Yu Long who was mentioned in ch 4) and that there's bound to be some movement happening soon. She hands SC a photo of one of the gang factions and it includes the familiar silhouette of a man without 2 of his fingers (guess who). Chapter ends with YW asking SC about the mole situation in TS's gang.