If anybody is up for a heartwarming story about the friendship between a spoilt noble girl and the ghost in her head, I would 100% recommend 取り憑かれた公爵令嬢（The Possessed Duke’s Daughter）!
It has happy moments and sad moments, and the characters are all pretty lively and likeable. Although there are a few clumsy parts, overall it’s a pleasant and enjoyable ride.
Despite the somewhat cliche-sounding setting, the execution isn’t so. For once thing there’s no romance, and for another it’s written in third person.
I enjoyed it enough that it enters my top ten web novels, and perhaps even top five, so please consider it. It does take the first fifteen-ish chapters to really start setting it apart from other novels though.
One other thing. Although it’s really easy to tell Lilia (the noble) and Sakura (the ghost) apart in Japanese, that probably isn’t the case in English, so in their internal dialogue, I would probably bold or italicise one of them.
Spoilers on why I actually liked it so much: