Thinking about the implication that Liko's family is rich, not just from the appearance of her house but also that she's not just attending an international academy but said academy is implied to be the Pokémon world's equivalent of a private school, which is usually very expensive to attend and pay tuition for.
Indigo Academy is definitely a private school. Its name in Japanese is セキエイ学園, which when read aloud transliterates to "Sekiei Gakuen". The term "gakuen" carries the nuance of a private school. Everything from the way Liko enrolled into Indigo Academy to how the school is structured reads of similarities to private schools in IRL Japan, especially international boarding private schools which do have international students. She had to go through an interview process to enroll, and when she does, she's living in a dormitory during her school life, which is akin to real life gakuen academies. They also have a specialized curriculum based in battling and being a Trainer, and it's owned by the Indigo League, which ties into the idea of it being a private academy.
So yeah, Liko comes from money alright.
It's also a contrast from the school in Vermilion City that Goh and Chloe attend since that's the equivalent of real-life public schools in Japan. It's called "gakko" (学校), and the way things are there mirrors public schools as opposed to private schools. Most likely in Goh and Chloe's case they're in real life late shogakko (小学校), as fifth years (gonensei).
I would guess Vermilion City in Journeys that they have a chugakko (middle school) and kotogakko (high school) too that are nearby and students move from the shogakko seen in Journeys to the nearest associated chugakko then koko.
Rambling but yeah, modern Kanto in the anime seems to incorporate real world school systems and we see both public schools (gakko) and private schools (gakuen) and a depiction of them that mirrors IRL Japan, especially since Kanto is based in Japan's IRL Kanto region which is their modern urban region with the big cities like Tokyo being there.
Just before, we had a few characters enroll in something akin to real world public schools, then Horizons has Liko attend what is essentially a private boarding school, and she's kinda unique among Anipoke characters in that regard, especially since it points to her being pretty rich to be able to attend a private school internationally.
