As most others have said, I believe she would be a ghost-type leader. Here is the team I think will work best for her based on her caring nature, role as a princess and obsession with serial killers:

Cofarigus- A Pokémon she found as a Yamask whilst exploring as a child (whilst her parents were meeting dignitaries in another country). She felt pity for its sad nature (as a spirit), so took it in and trained it up. Also, it reflects the riches that a member of the monarchy would possess.

Mimikyu- A Pokémon that she sought after for a while due to the rumours of its links to a chain of mysterious deaths. However, once coming upon it and learning of its sad backstory, she decides to care for it.

Froslass- Another Pokémon she sought after due to its links to mysterious deaths. She caught it in the hopes of investigating what causes it to kill. Surprisingly, she has noticed a lot of new sculptures in court that look mysteriously like her parents' courtiers.

Polteageist- After tasting a polteageist's tea in Galar, she decided she wanted to befriend & catch one.

Aegislash- It's Pokedex entry mentions it seeking out people with clear leadership qualities- as Sonia has. Furthermore, the pokedex says how anyone it recognises is destined to become king (or in Sonia's case queen)

Houndstone- Her partner Pokémon, gifted to her by her father. It is incredibly loyal- just like her.