Service will continue after closure eShop.

Following the news that Nintendo is shutting down the eShop for the Nintendo 3DS and WiiU in 2023; Nintendo has announced that its online Pokémon storage service (Pokémon Bank) will become free in late March.

Pokémon Bank is currently used to transfer Pokémon from Gen 1 and 2 (Virtual Console) and Gen 5 to Gen 7. (Remember you can transfer Pokémon from Gen 3 to Gen 4, and so on.) All the Pokémon from Pokémon Bank can then be transferred to Pokémon Home, which is the current main service to store Pokémon.

As of now we don’t have an end date for the Pokémon Bank service.

Source