I think the red soul represents regret, guilt, confusion, boredom, shame or craving
Why do i think its one of theese well
Regret cus we mostly want to try something diffrent and regret choises we have doen before. example is killing toriel, you can regret it and reload the save before it and avoid killing her after you learn how to mercy her and then flowey knows that you regreted killing toriel so he teases you
Guilt is almost the same as regret but you dont go back. this is more for the genocide run and you bear the guilt of killing so many monsters leading to fighting sans and also if you look at the mirror in asgores house it sais "Despite everything, it's still you"its just you and that you have always been you being either a murderer or not. you still bear the guilt for what has happend
Confusion beacause you dont know where to go. you dont know who or what your purpose is wandering the underground. you dont know how your life should end you dont knwo what end is perfect for you
Boredom since you cant find anything you want to do and the perfect ending you choose gencide since your bored. you choose pacifist since oyur bored of bieng a murderer and you choose neutral since you dont know what you want to do.
Shame is almost the same as guilt but more stressing. Shame is a feeling of embarrassment or humiliation that arises from the perception of having done something dishonorable, immoral, or improper. People who experience shame usually try to hide the thing they feel ashamed of and frisk hides that shame with his "poker face".
Craving since a person craves something like a family, a perfect ending, friends, blood and more. you crave excitment so you choose what you want and crave that you get what you want like murder or a fight with sans or ccraving the best ending or craving to go home since all frisk want is to go home
If you want to tell me what emotion you think the red soul is
My theory is that the red soul are more of negetive emotions unlike the others