I was trying to think of what trait Thursday and Mariella each got from each other for being literal soulmates, and I think I finally figured it out.
I already had Mariella's trait from Thursday figured out - it's that through the socket of her missing eye, she can "see"/feel what Thursday is experiencing at random times or during times of heightened emotional states. She can kind of "see" what Thursday is seeing, or get a sense of what is going on around her. So, like, if Thursday was lost somewhere, she'd be able to "see" her surroundings and get a sense of what she is feeling. It is both a blessing and a curse - it can be helpful in times of emergency, but it can be annoying (as you can imagine) during times when Mariella doesn't really need to be knowing what Thursday is up to, like if she is just sitting in the stairwell crying over a fictional character dying. xD The same works in reverse - Thursday can "see" and feel through Mariella's missing eye too, but it's not as strong going in this direction.
From Mariella, Thursday has gotten a sort of... therapy ability. It's kind of hard to put into words, but it's like, Thursday has a better understanding of how to help herself regulate her own emotions and boundaries, and also a better ability of helping others with the same thing. She wasn't really able to do that before. Mariella is very good at setting boundaries and also reaching out to people and empathizing with them in a healthy way. Gaining this trait from Mariella has really helped Thursday understand herself better, and helped her understand others better too. At least, it helps her with not taking this so personally and helps her to be able to move on from emotional upset quicker and easier.
It might feel a little unbalanced, like Thursday is getting more "benefits" out of it, but I think that's because in all technicality, Mariella's soul came from Thursday's. That's how the literal soulmates thing works. Whenever a Character in the Story dies, parts of their personality go into the meta ether to be formed into new Characters. When Thursday went to Dimension 42 and chose to die, part of her personality went into Mariella, thus making them literal soulmates. The same happened to Doomsday and James when Doom was in Dimension 42, although she managed to survive when she was kicked out and back into the living realm. It's the other way around with them, though - James gets the better end of the deal, but Doom is okay with that because he got the annoying part of her personality. xD