Pokemon HOME which is a paid app which allows users to manage the various Pokemon they have caught over a number of games and transfer them to Sword and Shield has a release window. You’ll be able to connect with Pokemon Bank, Pokemon GO, Pokemon Let’s GO Pikachu and Eevee, and of course Sword and Shield. However, these Pokemon need to appear in the Pokemon Sword and Pokemon Shield expansion packs which are The Isle of Armor and The Crown Tundra expansions.
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Note: Players who haven’t purchased an Expansion Pass can still receive Pokémon that will be added via The Isle of Armor and The Crown Tundra expansions through means such as trading through Home etc.
The real reason national dex won’t be fully appearing in any game is because of this. Gamefreak wants to hide your Pokémon behind a paywall. This is a paid service separate from Pokémon Bank and doesn’t come with NSO.