First take a look at Lucia's mother, Amanda. Amanda snuck Lucia and herself out of the castle and decides to hide in the country's capital, probably only a few hundred miles/km away from the imperial castle. Yes they were able to successfully hide in the capital but that also implies that the jobs that they did were not outdoors because outdoor labor would risk them being found by the members of the royal family which also implies that they probably didn't do any hard labor. The arthor writes that Lucia and her mother lives with some foster family for a short time and then her mother dies from a plague that spreads throughout the city. Lucia is later found after Lucia delivers a letter written by her mother, before her mother is about to die to the royal family, which results in Lucia to be brought back to the castle to start her supposedly new dream as noted by the synopsis. Lucia then reenters the imperial court as a courtier except she does nothing a courtier would do and instead hides in the castle like she is leveling up her sneak skills like she is going to be a master thief. What is most impressive is that her sneak skill is so high that she even manages to be invisible during church service, a public function that all royalty is pretty much required to participate in. In fact, Lucia's sneak skills are so good that she is even more elusive than a WIMP, Weakly interacting massive particles (quantum physics), and since there is no Large Hadron Collider (LHC) in that day in age, no one but God, aka the author, is able to prove that she exist which is what literally happens; She only shows herself when the writer says so; More details will clarify this fact later.
What the people around Lucia perceive about her at first is that she seems autistic but Lucia, being the legendary-tier thief that she is, doesn't do anything about it. I don't know about you but having autism isn't really going to help you in finding a spouse. Maybe you can argue that there are many stages of autism but the fact is that the rumors of her having autism have already spread and she makes no effort to disprove these rumors, like showing up at social events and actually holding a conversation with anybody.
Lucia is also born out of wedlock, which means her mother didn't marry the king, no church-held ceremonial service took place to declare the union of Lucia's mother and the late king (unless the church does postmortem marriages) which means she is a illegitimate child, aka bastard child, which means she isn't even a princess but at most a legitimized bastard. To be clear, being born out of wedlock implies that Lucia's mother isn't even a concubine, wife, or consort of the king.
Let's just assume that the king gave out the title in advance, well he's not dead at the time he receives the letter but he obviously can't marry a dead women unless the church allows a union between dead people which could be done in some religions, Lucia still had opportunities to go to meetings, festivals, balls (dance events), and even church service to show off herself; The importance here is to show potential suitors that she isn't autistic but nope, Lucia is too busy leveling up to be a sorceress leaving the rumors of her being autistic well in circulation. Maybe the king married Lucia's mother in their last seconds? But that would mean that Lucia would have to be present at the wedding which is held by the church which is a pretty big event since her father is literally the king of the kingdom and would give Lucia a huge amount of presence/publicity. Maybe said event does happen but Lucia acted like she was autistic which lead to the rumors of her being autistic? To be clear, said event might not of happened, I made it up to fill plot holes but the author does state that Lucia seems autistic at first when she enters the castle.
I know females act reserved when it comes to romance but there is a clear line between acting reserved and not even telling people you exist and the latter is what Lucia clearly does at her stay in the castle. I'm not sure how anyone is suppose to find her if she hides in her room all day. Maybe if Lucia does some singing, some prince might come along and at least hear her singing which would be a pretty good start even if she can't sing well; Rapunzel reference for those who don't know. When it comes time for her to be married off, she is disappointed that her brother, now the 9th King of Hesse is going to marry her off to some hedonist count after said count won the auction. The fact here is that even if the king was still alive, the current king is the 8th king of Hesse and Lucia's father, would still have to marry her off. Lucia's father might not use an auction system but the fact that he wasn't able to find any suitors means that either he was too busy, no suitors wanted her, or Lucia couldn't compete with the competition, or a combination of said options; Maybe she is waiting until the internet to be invented so she can just use dating sites? Her brother marrying off siblings in his court is proper and something he is required to do anyway, unless you think that Lucia can just leech off the royal family forever or maybe she really is trying to be wizard; If you're going to be a wizard, you better be a F-ing wizard. As stated earlier, her brother and potential suitors all think she is autistic or rumors of her being autistic make it really hard for Lucia to get arranged with suitors that are par/sub-par so she has to settle with the worse of the worse, some hedonist count. If her father, her brother, and suitors knew that she was not autistic that would greatly increase the chances of them trying to find a good match. I don't know about you but I'm pretty sure you would use a reporting agency when you are about to purchase a car from a re-seller and this is exactly what the bidders do, they ask around for the historical equivalent for CarFax and probably learn about rumors of Lucia being autistic, not a very good trait for your children if you ask anyone. Maybe if Lucia actually appeared at social events which would build her presence/popularity, and also serve to disprove the fact that she is autistic then none of her problems, problems that she caused herself, would of happened. Also, if Lucia's mother did not take her out of the castle then Lucia would of had time to educate herself, be known among peers, advertise herself, and maybe even get a suitor to ask for her hand in marriage in front of the king.
I feel like the novel has no consistency. The author makes Lucia's value during her time in the royal castle next to nothing by giving Lucia the curse of silence, it's like the same curse that happens to the Islamic version of Mary Magdalene (True fact and you can read about it by Googling the search phrase "First Miracle of Jesus in Islam", make sure its the Islam version because the numbers don't match in the Christian version) except there is no talking baby Jesus and Lucia's curse also comes with autism, Thanks God!
Lucia spends all her time doing nothing and just relaxes all day and just expects handsome men to come ask her hand in marriage. It's like she read Sleeping Beauty and expects something similar to happen to her; Fun fact, the original version of Sleeping Beauty and variants include either the prince having s*x or raping the sleeping princess, maybe Lucia is into sleep fetish?, which results in the sleeping princess bearing children so maybe she expected that too; Disney wasn't even born yet so the G-rated version doesn't exist yet or maybe it does exist and she hopes that the G-rated version happens to her. She clearly does nothing to change her fate while at the castle despite the synopsis saying she does something; Maybe she does some closed-door cultivation while in the castle to become a Taoist Immortal? Anyway, no surprise later when all her dream of just chilling and relaxing every day for the rest of her life, her foster family were clearly Timon and Pumbaa from Disney's the Lion King, "hakuna matata", It means no worries for the rest of your days; is crushed after no one really wants her and when her brother tries a last resort option of auctioning her off to be married, far better value than just having her eat, sleep, and do a good job at being a liability, the next thing you know, she is all healed by some divine being (cure for autism found!), she suddenly changes her behavior, gains a ton of awareness, and actually has an ambition for self-improvement. I wouldn't be surprised if she uses her legendary-tier higher invisibility to sneak out of the castle since it seems to be a hereditary trait/skill. The story would also be more believable if Lucia died from the thought of marrying a hedonist count and someone transmigrated into her body thus dramatically changing her character because this is what exactly happens.
There is also the option of being disowned by the royal family and marrying a lowborn aka commoner. The number of suitors may increase, obvious fact that commoners greatly outnumber royalty = more suitors, which means she can pick from a larger number of suitors but why give Lucia all the presence in the world when she is among the commoners and none when she is among royalty? Maybe she can request her brother, Lucia's brother is now the king and has the authority to request excommunication, to be excommunicated by the church, because no one ever sees her at church which is a very valid cause for her excommunication, which would allow her to marry a commoner because excommunication also is also a acceptable clause to disown and exile someone.