
Allow me to explain (●'◡'●)ノ
Horoscopes, also known as astrological and/or natal charts, refers to the prediction of events based on the location and movement of the celestial bodies, including the Sun, Moon, and planets.
Such events include birthdays which determine an individual's astrological sign. For example, Haesoo was born on January 30th (as stated in chapter 21.5), when the sun is positioned in Aquarius. Therefore, his Sun sign is Aquarius. So what does this mean? Well, Sun signs supposedly represent our conscious mind or ego based in reason rather than instinct. In other words, it's our basic identity.
As an Aquarian, Haesoo is individualistic, assertive, independent, original, eccentric, intellectual, idealistic, cool, and friendly but detached. He is growth-oriented and "unwilling to follow the beaten track". I could go more into the characteristics of Aquarius (as I'm one myself) and why I think it fits Haesoo, but we'd be here all day. However, if you want to know more there's plenty of resources online.
Leos (Joowon's sign) are known for their regal qualities, and are thought to be strong leaders, which also means they are reputedly conceited and authoritative. They can appear lazy at times, but they're actually hard-working when it comes down to it. Leos are generally motivated by affections towards other people, so they have big dreams/plans to make people happy. But they have a tendency to hold onto situations and people for too long. Sound familiar?
As for Scorpios (Taekyung's sign), they're known for their intensity, determination, and perceptiveness. They throw themselves into whatever they do; their primary motivation, "real" power different from prestige or authority. Scorpios know what they want, but they're patient and strategic in how they get it. They're not afraid to explore the "darker" sides of life, and because they have tremendous willpower, they never give up and aren't intimidated. In my experience, Scorpios are the hardest sign to guess because they tend to be private about things.
Anyways, I think these signs are very fitting for these three. Of course, Sun signs are not all-encompassing (there's also Moon signs which represent inner self), and whether you believe in it is up to you. I find it's a fun way to pass the time and contemplate the world. As for compatibility, well yes, there are some horoscope writings out there which discuss compatibility of sun signs, but there too many other factors for it them to be determinate imo. If you read all that, congrats! Have a cookie :)
Haesoo - Aquarius
Joowon - Leo
Taku - Scorpio
Personally, I think the author thought this out because, to me, it fits.