The spring of 2023, specifically
So now that Pokemon Scarlet and Violet are in full swing, people are going to want to transfer all of their old characters in. Well, you’ll have to hold off on that! That functionality isn’t coming until roughly mid-2023.
Here’s the full confirmation of when Scarlet and Violet are getting Home support
So over on the game’s official site, The Pokemon Company says that support will be coming “in spring 2023.” It’s important to remember that this will only include “select Pokemon from past games” as well. Here’s the disclaimer: “Note: The Pokemon you’ll be able transfer to each game via Pokemon HOME are limited to Pokemon that can appear in those games. Please look out for more information about which Pokemon will be available in Pokemon Scarlet and Pokemon Violet.”
Before then, there is something coming sooner. That same post explains that in “early 2023,” the pair of games are getting “Battle Stadium statistics” support: “From the app, you’ll be able to view information about Trainer rankings, frequently used Pokémon, Online Competitions, and more. You’ll also be able to see what moves, Abilities, and held items are being used in battles the most.”
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It’s unfortunate that the rollout is so far away, but it also allows for some time for the current generation to marinate and sink in, without tons of different metas emerging. Its also plenty of leeway to get a full living Pokedex in Scarlet and Violet.