I am assuming winds and waves will have HOME compatibility here
If you don't bother looking at the chart here's a text version (this took me a hour to write)
Pokémon Red and Blue ↔ Pokémon Gold & Silver
Pokémon Stadium ← Pokémon Red and Blue ↔ Pokémon Stadium 2 ← Pokémon Gold & Silver
Pokémon Red & Blue → Poké Transporter ← Pokémon Gold and Silver
Pokémon Ruby & Sapphire ↔ Pokémon FireRed & LeafGreen
Pokémon Ruby & Sapphire ↔ Pokémon Box Ruby & Sapphire ↔ Pokémon FireRed and LeafGreen
Pokémon Ruby & Sapphire ↔ Pokémon Colosseum ↔ Pokémon FireRed and LeafGreen
Pokémon Ruby & Sapphire ↔ Pokémon XD: Gale of Darkness ↔ Pokémon FireRed and LeafGreen
Pokémon FireRed & LeafGreen → Pokémon HOME
Pokémon Colosseum ↔ Pokémon XD: Gale of Darkness
Pokémon Ruby & Sapphire ← Pokémon Colosseum (Bonus Disc)
Pokémon Ruby & Sapphire ← Pokémon Channel
Pokémon Ruby & Sapphire → Pokémon Diamond & Pearl ← Pokémon FireRed & LeafGreen
Pokémon Ruby & Sapphire → Pokémon HeartGold & SoulSilver ← Pokémon FireRed & LeafGreen
Pokewalker ↔ Pokémon HeartGold & SoulSilver
Pokémon HeartGold & SoulSilver ↔ Pokémon Battle Revolution ↔ Pokémon Diamond & Pearl
Pokémon HeartGold & SoulSilver ← Pokémon Ranger → Pokémon Diamond & Pearl
Pokémon HeartGold & SoulSilver ← Pokémon Ranger Shadows of Almia → Pokémon Diamond & Pearl
Pokémon HeartGold & SoulSilver ← Pokémon Ranger Guardian Signs → Pokémon Diamond & Pearl
My Pokémon Ranch ↔ Pokémon Diamond & Pearl
Pokémon Diamond and Pearl → Pokémon Black & White ← Pokémon HeartGold & SoulSilver
Pokémon Diamond and Pearl → Pokémon Black 2 & White 2 ← Pokémon HeartGold & SoulSilver
Pokémon Black & White ↔ Pokémon Black 2 & White 2
Pokémon Dream Radar → Pokémon Black 2 & White 2
Pokémon Black & White → Pokémon Dream World ← Pokémon Black 2 & White 2
Pokémon Black & White → Poké Transporter ← Pokémon Black 2 & White 2
Poké Transporter → Pokémon Bank
Pokémon X & Y ↔ Pokémon Bank ↔ Pokémon Omega Ruby and Alpha Sapphire
Pokémon Sun & Moon ↔ Pokémon Bank ↔ Pokémon Ultra Sun and Ultra Moon
Pokémon X and Y ↔ Pokémon Omega Ruby & Alpha Sapphire
Pokémon Sun and Moon ↔ Pokémon Ultra Sun & Ultra Moon
Pokémon Bank → Pokémon HOME
Pokémon HOME ← Pokémon GO → Pokémon Let's Go Pikachu & Let's Go Eevee
Pokémon Let's Go Pikachu & Let's Go Eevee ↔ Poké Ball Plus ↔ Pokémon Sword and Shield
Poké Ball Plus ↔ Pokémon Go
Pokémon Sleep ↔ Pokémon GO Plus+ ↔ Pokémon GO
Pokémon Let's Go Pikachu & Let's Go Eevee ↔ Pokémon HOME ↔ Pokémon Sword and Shield
Pokémon Brilliant Diamond & Shining Pearl ↔ Pokémon HOME ↔ Pokémon Legends: Arceus
Pokémon Scarlet & Violet ↔ Pokémon HOME ↔ Pokémon Legends: Z-A
Pokémon Winds & Waves (presumably) ↔ Pokémon HOME
Pokémon HOME ↔ Pokémon Champions
by Fun_Illustrator_5332