Hi Gabe,
I would repot now since the container is too big and too deep, moving it to a right sized container, shallow better than deep, just put it in part shade, but not indoors, it still thrives better being outdoors. Actually I mist around the plant, not on the plant itself. I just do it to help cool down around it, and have learned to shade them now during summer. Or even if I happen to drench the plant, with our ongoing heat here, it dries out quite fast outdoors. But summer is such, blanket heat everywhere, so just be mindful of watering, once a week or so, allowing the water to drain out of the drain holes, and leave it alone in part sun-part shade. There are several types of semps, and some are more tolerant of heat, some are not, just have to see which ones they are that will work in your area. But in general , they are alpine succulents that love cool sunny days. Adjust your watering when you notice your temps are changing as seasons change, as it gets cooler, longer interval.
Just continue removing old dried out leaves, and you have seen the pictures of my semps, you need to make your media as gritty looking like that. Those roots need to dry out and breathe after watering. That is why we keep advising you to put more pumice/ rocks/ perlite in your soil mix.
