Man, that thing keeps chugging! Great news for JAXA, I wonder what additional science they're getting out of it. I know that we would have used any extra time for further downlink. So much data, such little bandwidth!
Probably environmental data, mainly temperature, and of course, they get to see how it progressively fails. They're starting to see some temperature sensor and battery issues for instance.
I took a look at the press releases and I can't see a lot of information about payloads, but if they're operations were anything like Nova-C (which I worked on), then they generated lots more data on landing than they could downlink at the time.
I would suggest main value is in seeing how this thing still lives! It was designed for one lunar day and has survived 3. So for learning about what still works and what doesn't this is invaluable for future reliability engineering.
In this case there does not appear to be any public evidence that they did much testing in below freezing temperatures. This isn't to say that they couldn't do the testing, just that they didn't do it because the mission parameters did not require it. There don't seem to have been many "ongoing experiment" type sensors on the lander which would be significantly useful to keep going longer than the initial mission.
As for radiation, I attended a lecture series last year about the various kinds of radiation testing involved in designing hardware for satellites, they probably did do similar things to those for satellite electronics (stuff like firing beams of IIRC electrons over the PCBs to see what parts might need reinforcement/redundancy against random charged particle strikes).
Part of the unknown is likely what temperatures, how much radiation, of what kinds. The SLIM lander can land in places previous automatic landing systems couldn't, so it's very possible this area has never had such measurements done. There's still much we don't know about the moon, including how cold the lunar night actually is in different areas.
Also, the point of SLIM was to test the new automatic landing system, a combination of camera-based navigation and a new landing strut system meant to handle inclines. 100 meter precision instead of previous 20 km. Everything that comes after that is near-free extra data.
