Her being the one that solely gets pampered is a trend that will last for like 3 or 4 more chapters. This is ultimately a revenge story to the very end and I don't really want to spoil (you can find the spoiler thread if you want), but she does ultimately get more active as she grows.
Your second paragraph confuses me. I think there are already some manhwas / mangas that stick to that concept, like leaving the house and pursue their career like that stationery lady, and that blue haired imperial chef FL. There's also probably other titles that have your mentioned plot, I just don't remember those long ass titles. What I mean is it's not really that rare, you just need to know where to find it.
Also here the white haired duke's people are those who are so fed up with the crown princess and despise the emperor. The duke seem to be close with pink haired FL's parents despite rumors of the two houses clashing with each other. Also I remember somewhere that she's the one who's supposed to be the real protagonist in this timeline, not the princess. She just naturally has that charm around her. When near the princess, the princess just kinda stole the spotlight from her.
But the difference between her getting pampered and the princess is that she knows it's unjust favouritism and is trying to rectify that
...a bit ironic with how the premise of the story is the mc going into a world where everyone pampers the protagonist but everyone else is ignored... when in fact the same thing is happening to her. Idk I liked the beginning but I knew it'd be mediocre when it comes to its concept from the start just from the fact her hair is pink. Not brown, because let's all be honest the majority of ignored characters have brown hair for the sole fact its the most common. Beautiful hair colour, my favourite in fact but its, most of the time ignored in manhwa just cause it ain't unique. Albeit you do find brunette flu don't get me wrong.
I kinda wish someone would actually make a story with the concept and sticks to it a bit more. Sure a romance aspect here or there is good but I wouldn't want it to be central either. I wish they'd do something a bit more realistic, yes fantasy isn't realistic but I mean like... how people are. Idk maybe have a male protagonist who ignores the mc and seems to hate her when in truth he has conflicting views... desire, obsession, a want to monopolise but he can't do any of that. Then he realises he likes the mc after a looongggg time. That type of romance I love eye reading about. And then maybe the mc ends up following her parents' wishes and goes off to marry someone of their choosing. A nice, decent, handsome young man of a fine background.
Or even idk she ends up actually leaving, or pursuing a career. Or even going to the countryside and living her life there finding treasures and discovering some ancient history, meanwhile training her prowess.
Idk people might think it boring but if done well it would be absolutely beautiful.
As for this story... its a fun read, I'll probably enjoy it but the fact that the mc disses the princess but doesn't see that she's the same as her kinda ticks me off. I don't like the princess either she's immature but a more truthful protagonist would be of greater liking.