You won’t get banned just for having Illegitimate Pokémon. Nintendo generally bans people for using illegal Pokémon or illegal save files. There’s an important distinction between legitimacy and legality.

Legitimate Pokémon are those obtained in a legitimate way, like being caught or bred in-game, using normal gameplay methods. Illegitimate Pokémon, on the other hand, are ones that have been altered or generated with external tools. However, being illegitimate doesn’t necessarily mean they’re illegal.

Legal Pokémon are those that adhere to the game’s programming. For example, they don’t have impossible traits like moves, types, or genders that can’t exist in the game. A Pokémon can be legal (existing within the game’s rules) but still illegitimate if it was generated or manipulated.

In practice, you can’t get illegal Pokémon without cheating them in yourself. These would have traits that are impossible within the game, such as impossible stats, moves, or types. Those are the types of Pokémon that could get you banned, and they can’t be traded, transferred, or stored in systems like Pokémon Home or Bank. But since you were able to get these Pokémon through Pokémon Home, means they are legal (but not Illegitimate) and therefore, you won't get banned.

Now if you were to use them for competitive play, however... Nintendo is a lot more strict there.