Thanks ! The led was effectively interfering. However, it still doesn't work...
I tried but it doesn't seem to be a problem.
Therefore, i will do more tests this week (It may be 33 IOT arduino which isn't compatible).
If you have any other ideas, please tell me.
The only thing that comes to mind, besides power issues which I've already mentioned, is running the two sketches on a regular Nano. But I'm not sure what that would tell you. If you get the same results on a regular Nano, you're still no closer to finding the problem. Anyway, I just hope you have made sure the voltage on the SD module's Vcc pin is not drooping when you are writing to it. You said something about powering it from a battery through resistors, which sounds very dodgy to me, and which isn't what your schematic and pcb image show. If I think of anything else, I will post about it, but I think I've run out of ideas. I've never used that Nano IOT or the SAMD21 processor before, so have no relevant experience to bring to this.