What, in your mind, is the point of having gender-based categories for sports?
Because taller people have proven physical advantages in basketball, but we don’t have height categories in basketball. Heavier people have proven physical advantages in fighting sports and we do have weight categories in fighting sports. Adults usually have proven advantages over children and in most sports children have their own competitions. But the minimum age for gymnasts in the olympics used to be 14 and was changed to 15, then 16 - what changed about 14-year-olds during that time and why is it 15 for figure skaters? And it’s pretty damn obvious a 50-year-old is never going to win an olympic medal in nearly anything (there are exceptions) but we don’t have a separate 20-30, 31-40 and 41-50 category. Of course at non-olympic levels there are sometimes age categories (I once met someone who had the world’s second best time in some length of breast stroke for people aged 65-69).
How we divide people into categories to judge them against each other in sports is a social decision made to address social conditions. There is no empirical right answer, it depends on what we are trying to achieve. Currently we have a state where people are allowed to compete as members of their own gender, without being singled out as trans. We also currently have a state where transgender people with olympic gold medals earned those gold medal before coming out (I say with moderate confidence). What is the real-world social problem with that state that would be solved by creating four categories as you suggest? Who is currently being treated unfairly and by what standard of fairness? (Or, alternately, since I think this is usually the way these decisions are made: How would that increase the number of people who are inspired to participate in sports?)