Nintendo confirms 3DS and Wii U online functions to be wound up from April 8th - Pokémon Bank and Poké Transporter to continue operating for now
After this date, users of these consoles will no longer have access to online play, internet ranking, or other data distributions for the majority of 1st party Nintendo titles, including Pokémon games. The sole exceptions to this shutdown are Pokémon Bank and Poké Transporter, which the announcement Q&A posted to Nintendo of America's support site explicitly notes will continue to operate.
Players who still have unused Nintendo eShop balances will only have until March 11th to merge this balance with a Nintendo Account, to allow for the balance to be used on Nintendo Switch systems.
This sunsetting of features explicitly does not include remaining eShop functionality on either the 3DS or Wii U consoles, and at this point in time, Nintendo has stated that users will continue to be able to download update data and redownload any previously purchased digital games for the forseeable future. Given that it's still possible to download Wii titles, roughly half a decade after the Wii Shop Channel closed to new sales, it's likely that purchases will remain available for download for many years to come.