catra's assholishness was starting to get tiring during season 2. her character arc and relationship with adora remains the heart of the show, but it was the same thing iterating on top of itself after having season 1 full of it. the only difference was that catra was the one in charge of hordak's forces.
season 3 actually did something with that. catra's accomplishments - becoming force captain and leading hordak's forces with efficiency, were undone by her desire for approval. she enjoys the power and authority, and really enjoys rubbing it in shadow weaver's face to show that she actually did accomplish something, but it doesn't give her what she really wanted. she wanted shadow weaver to appreciate what she did, and that didn't happen. later when she becomes leader of the crimson wasteland, she has power and authority which she gets to hold over adora, but she also is quite happy for once. she accidentally achieves something for herself that she enjoys. this is now undone by her seeking approval from hordak, leading to a disastrous end for all those around her.
watching catra succumb to azula-style rage was a lot of fun. seasons 1 and 2 saw catra being downright petty because of perceived betrayal from adora. it almost feels playful. catra still cares about their friendship, which is her motivation to 'get her back' for abandoning her. in return, adora still obviously cares about catra, and that's constantly apparent in their interactions, and catra knows it. the stakes - killing the princesses, taking over the world, destroying the world - they're small potatoes compared to her friendship with adora. even on opposing forces, catra's interactions with adora still give her something resembling their former friendship. it's not until she-ra returns from the alternate reality that it's clear catra fucked up. catra's severed this relationship completely, and both she and adora know it.
one of the interesting things about season 4 will be how catra deals with the true loss of her friendship. if adora is no longer pleading with her to cut things out, i imagine catra's motivation won't be driven by a desire to get something out of a former relationship, but out of a deeper hurt and possibly self-loathing.
going forward, i do expect some level of hordak turning over to the side of the princesses. it seems that a common thread is to not build your relationships on the approval of other people, but to be your own person and surround yourself with people who like you. hordak is seeking his own approval from hordak prime, and has now developed a fledgling friendship with entrapta - this will provide the building blocks for his turn against hordak prime.