Set harsh restrictions on transferring Pokemon into Let's Go. Cannot transfer any Pokemon that has been in Sword/Shield to Let's Go, even if originally from Let's Go. Likely holds true for Brilliant Diamond/Shining Pearl to Let's Go too. Has to do with abilities or something. Prevents Pokemon from Bank -> Home -> Let's Go for similar reasons...probably. (Note: Not an expert on this.)
Should still be able to transfer from Let's Go to Home and back to Let's Go, provided no other stops along the way. Could also trade for usable Pokemon from the phone app, assuming proper eligibility. (Displays that information in the phone app. Go to the GTS. Choose a Pokemon, then hit "Games". Pick the Eevee and Pikachu faces.)
For the other Pokemon:
- Raikou and Suicune: Sword/Shield and Brilliant Diamond/Shining Pearl
- Reuniclus: Sword/Shield
(Tried searching them in the phone app. Showed only those possible games for them.)