I’ve searched around quite a bit for info on the SD card but I can’t seem to find answers.
Does the Opensprinkler 2.1u come with an SD card?
No. There’s the slot, but not the microcard. At least my specimen came without card.
What type of SD cards are supported? What role does the SD card play?
Do not know exactly. Microcards FAT32 formatted, if (my) memory serves.
Others may answer here
Is it required to power on and use the device or is it only there if you run out of space on the Atmega?
No, is not essential. My OS have been running a couple of months without card.