In the 2nd timeline they discuss that because Aeroc was given his titles as an alpha, if he is revealed to be an omega, others may try to legally strip him of his titles. By marrying openly and having kids he may lose his wealth as well, so Aeroc and Kloff hide their true relationship and their kids' origins. Well in the 3rd timeline, the same thing stands, however in that timeline Aeroc is more headstrong and mentally sound compared to the 1st and 2nd timelines. One of the conditions to being with Kloff is that they won't have kids because it would risk Aeroc's titles, and he can just adopt an heir. Also pregnancy is dangerous for male omegas, so he doesn't want to have his own kids. If Kloff truly wants to be with Aeroc, he has to change and compromise.
Season 1 is a mix of the first timeline and the 2nd one, but you get glimpses of the 1st timeline throughout. The final season is the main ending (where Aeroc with his past memories gets together with Kloff who does not know of the 1st timeline). The side stories cover Aeroc's first pregnancy and some of the 3rd timeline. None of the What If stories have been adapted yet. I will say that the worst part is the beginning in the 1st timeline, it's honestly super painful to see Aeroc suffering. The rest of the story is more chill.

As for clarification without major spoilers, this story surrounds 3 timelines. The first one is where Aeroc dies after being assaulted, and he wishes to make up his wrongs before he dies. Kloff lives on and raises his kids but struggles to raise them because they start questioning who their actual mother is. Kloff dies wanting to see Aeroc again. The second timeline is where Aeroc remembers the past, and he wants to make up his mistakes by helping Kloff get together with Raphael. Kloff doesn't remember the past but he does get flashbacks that he thinks are dreams. In the third timeline Kloff remembers the past and initially thinks he is in hell. However, he actually scares away Aeroc, who doesn't want to associate with Kloff anymore because of his rude behavior. Aeroc doesn't remember the past, but they do get close.
Spoilers.
So in the first timeline, Kloff's oldest child exposes what Kloff did to Aeroc. And Kloff is left alone at the end. In the 2nd timeline Aeroc tries his best to make up for his mistakes, but although Kloff does not marry Raphael, Raphael does marry Wolflake and lives a happy life. Sadly, Aeroc never gets to meet the children from the first timeline. In the third timeline, Kloff finally admits his feelings and stops being a dick to Aeroc. He's even willing to die because of their bond than to hurt Aeroc again. In this timeline Aeroc does not want kids, and so neither of them meet their kids. Kloff is haunted by the fact that he can't ever make it up to the original Aeroc and has to accept that they won't be seeing their kids to make it up to them as well.
Now there is an interesting what if story where Aeroc survives his assault from the first timeline. Kloff actually treats Aeroc better and Aeroc gets to meet their kids. They eventually move away and live a better life.