Questions, answered

Moving a Pokemon from one game or storage service to another. Depending on the era this happens by trading over a cable, migrating through an in-game area, or moving boxes through a cloud service like Pokemon Bank or Pokemon HOME.

Use the Route Finder: pick the game your Pokemon is in now and pick Scarlet & Violet (or wherever you want it). It will lay out every step, including any subscriptions or hardware you need.

Some steps require a subscription: Pokemon Bank (annual fee) for the 3DS era, and Pokemon HOME has a free tier plus a paid Premium tier needed for moving from Bank to HOME and for larger storage.

Generations I and II are sealed off from Generation III onward (the Great Divide). The only workaround is to re-obtain the Pokemon in the Virtual Console re-releases on 3DS, which can reach Pokemon Bank.

Usually no. Most transfers are one-way "ratchets". Link trading within a generation and Bank/HOME deposits are the main two-way exceptions. Plan your final destination before you climb.

Held items are removed on most one-way migrations, and some hidden values can reset. Moves and ribbons generally survive. See the "What Gets Left Behind" guide for the details.

Only if that game recognizes the species. Modern games use regional dexes, so you cannot withdraw a Pokemon into, say, Sword if it is not in the Galar dex.

Yes - GO sends one-way into Pokemon HOME via the GO Transporter, and Kanto Pokemon one-way into Let's Go via GO Park. They can never return to GO.

Send any Pokemon from GO to Let's Go (or HOME). This rewards a Mystery Box, which makes Meltan appear in GO for a limited time.

Bank is the 3DS-era cloud (two-way with Gen VI/VII). HOME is the Switch-era cloud (two-way with the Switch games, and it receives from GO and Bank). Bank can send up into HOME one-way only.

If you have Pokemon stuck on 3DS games or the Virtual Console titles, yes - Bank is the bridge that lets Poke Transporter feed them up toward HOME.