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Gio is adopted right so, Lee Gang and Gio are brothers (not sure if half or full). Lee Gang is not interested romantically with Giovanni, but I think Lee Gang knows that Gio and Felix are dating after he saw Felix's wallet (he might have investigated or something). Since Lee's mom is still attached with Gio, Lee wants to find him and reconnect with him. I think the next chapters might reveal Gio's childhood family experiences and more childhood memories with Felix, specially between their moms.
Since Taehwan is not too attached with Yeonwu, he will find himself being with a girl. Another guy comes and gives attention to Yeonwu, and that will trigger the hell out of Taehwan but he couldn't do much cause he is a coward when it comes to recognizing his feelings :>