my N3DS would not boot with a some luma error
Don't you think it would be helpful to provide some details there? Surely you don't think you're the first person
ever to see whatever error you're seeing?
I can't boot from the old card with the nintendo 3ds folder from the SD card.
There are some cases where the Home menu extdata or theme data can get corrupted, in which case the solution is to clear that data, as discussed at the bottom of
https://3ds.hacks.guide/troubleshooting . But those problems will not cause "some Luma error".
If you're getting an error message about the "boss" process, then unfortunately no one really knows what causes that error, but you shouldn't have to start over with a fresh SD card. Standard procedure is to copy everything off the card (
Roadkil's Unstoppable Copier is suggested), format the card, test the empty SD card with h2testw, and then copy everything back to the card again if the test is okay. You wouldn't expect that to do anything, but sometimes that is enough.
Alternatively some people solve the "boss" error by doing a firmware update in safe mode. (This will not affect CFW.) I should also add that the "boss" error will go away if you disable wifi, which would at least let you access Checkpoint if you want to do things that way.
Regardless, if you're just concerned about your Tomodachi Life save data, then since you haven't formatted the 3DS at all, you should be able to copy the save file off the SD card directly and onto another SD card. (These files are encrypted, but you're not changing the encryption at all in this case.) The file will be stored in /Nintendo 3DS/<ID0>/<ID1>/title/00040000/0008C300/ , as per
https://hax0kartik.github.io/3dsdb/ .