Hey! I worked at a place that made microgreens a while ago, so I might have some input to share:
What helped us keep rotting minimal was, before starting to cut them, let them dry out in front of some fans for a while, not until completely dry/essiccated, but just until, when passing your hand through them, you don't get it wet/damp anymore.
below, a picture I still have of some grown daikon, purple and pink radish microgreens drying out, all to be cut for the day's deliveries:

After cutting them, we used big airtight plastic boxes to store them, but every ~3cm height of microgreens, we layered in some paper towels to keep absorbing moisture even when put inside the fridge. We could use them as-is for the day, or as stock for the next couple days' worth of orders, in which case we spread them out and let them air dry a bit (near a fan if necessary, but not directly in front of it) before individually boxing them up in smaller single use plastic boxes for the delivery.
It was not unusual to use friday afternoon's cuttings for monday morning's deliveries, and with the air dry step, the condensation formed inside the fridge was almost a non-issue. (we would still get the occasional bad batch that stank after just a day, but that's just the mold lottery for you)
We did all kinds of other microgreens too, btw, so feel free to ask anything :)



