Will the local save transfer at start up automatically transfer ALL my saves?

I have a big SD card in my Switch 1. 256, I think. I have a lot of games saved on there. Will the Switch 2 take them all even if the SD card on the 2 isnt big enough? Will it take the save and game anyways but just archive them both since not enough space on SD card?

I just want to make sure I don't lose save data to the void for some reason on transfer.