Chandrayaan-3 rover and lander in sleep mode but might wake up later this month

Can't find what batteries they use. As long as they are dry cells, low temp should not permanently damage them. No battery functions below 200K, but damage is another question. When they warm up in the sunshine they should start functioning again, but the circuit boards are not so durable.
Keeping the batteries and electronics warm is a function of how much $$ you want to spend. India already met their mission objectives, no need to come alive in two weeks. If it wakes up it is a bonus.
Agreed that the mission already met its design objectives. But, from what I have read, they are still looking at the data acquired to see if they can detect water. If they do that with the existing data, then they have also met the hoped for scientific objective of going close to the pole. But, if not, another lunar day to go looking into a shadow would be needed to really evaluate the potential for water in the vicinity.
Yes, it would be nice to detect water in the data.
Since they are not in permanent shadow, there is no reason to expect any more water than any other sunlit place, 10-1000 ppm.
I don't know how far the rover is from a permanent shadow. Maybe it can get there if it wakes up.