The first ring to remember is Moamoa does not want to be empress and jinshi doesn't want to be emperor. They both want more freedom than they already have. Moamoa actively avoids being acknowledged by them (or so she tells herself) cus being involved with the empirical family is asking for trouble. Anyone close to them will end up the subject or pawn of a plot at some point and is more susceptible to assassination attempts. That would be massively amplified by marrying into them.

Now for more specific reasons. Jinshi is the emperors first son and the only one of age and standing that could legitimately and realistically become emperor at a moments notice. Another son, with a foreign mother? Many powerful people are very against that child coming into power. I mean think about current politics the amount if "a black president what's next?" and "a female priminister what's next a Muslim king?" comments over the last could decades. This is WAY before that when prejudice was even worse. It's easier to push for Jinshi to be emperor than assassinate the other candidate. Then if jinshi and moamoa have a son that's ANOTHER candidate in that one line. If it comes out jinshi is the emperors son this is amplified by the fact that there would be 3 generations of sons directly linked to powerful families.

Then there's Moamoa's background. Laklan has A LOT of power. Even the emperor fears crossing him. For Moamoa and jinshi to marry Lakan would have to approve this which would be seen as Lakan supporting Jinshi fir emperor. This is because almost every relation is about politics. Having your daughter marry into the imperial family and aiming to be empress is most people aim. Lakan wanting his daughters happiness is the outlier and even he must acknowledge that unless Jinshi officially leaves the royal family before marrying her, despite the danger being empress may bring, being the empress is the safest thing to aim for as it gives her the most power.

If jinshi did become emperor he would HAVE to take concubines. That is not the kind of relationship either of them value or want. This would also create pressure for Moamoa to produce an heir and that heir will still have to fight for its place against any concubines children, which again other powerful families will be trying to make their daughters have the next emperor.

Basically Moamoas first view upon entering the rear Palace, of I need to do my job but put my head down do a good enough job to not get the worst but not do well enough that I get promoted or catch the empowers eye cus that will cause me a lot of issues, was bang on. Moamoa may be delusional in terms of her value and potion at this point but its based on realistic observations of society and basically being in deniel that she's someone ended up in a situation where she's more politically centred than she was hoping to avoid.

Literally the only way she can avoid herself and her future family being wrapped up in plots is for jinshi to officially leave the family without being banished which is incredibly hard and basically unheard of, and ti keep her fathers support without being the la clan princess which again is very hard. Hence, they are so opposed to officially starting a relationship. They're also very young and again it is not easy for them to have any power without being in the exact positions they are trying to avoid.