Hi Everyone, need some advice on the plant condition.

I was wondering is that root rot?

Prior to this, the plant was in a small pot for approx. 3-4 months. I recently took it out because some of its leaves started withering. Two things come into my mind:
1) My plant was potted 3-4 months ago, the roots did not seem to have grown at all
2) Secondly, whenever I bottom watered it I can see my plant being plump and healthy. So not sure if the roots are unhealthy.

Thus, a little confuse if the root is having problem based on what I am seeing here.

After letting it air dried for a few days, I repotted it. Within 2 weeks, i see the leaves drying up although i had only just watered it a few days back, probably after 3-5 days after repotting (see 2nd picture).

Appreciate if any experts out there can provide some feedback what is happening here. Thanks in advance!

I can't see rot, but the roots look compromised to me. To the point it essentially has no roots. It can/will grow new roots and thrive again if handled correctly. That's usually a sign of overwatering. Does that pink container have a hole? Drainage is essential. Was it in that container before you took it out? The soil looks a little too water retentive in the photo, but I can't be sure. Lay the plant on a shelf for a few days and let it dry a bit and then plant it in a small container with a drainage hole and be extra careful not to allow the soil to stay damp for long periods. Let the soil dry out and then give a good watering. I wouldn't do a lot of that, though, until you see new growth in the rosette. The plants has a residual store of what it needs to grow new roots, so it may wrinkle and wilt a bit before they are growing but it should do if you are patient. If you are in a geographic location where winter will soon onset, you'll need to be even more careful about watering durng the shorter days of sun and cooler temps. I've had unrooted plants like that and didnt give them ANY water during the winter months. They are still around after a few years. Good luck!

Donald has given some really good advice. I would only add (based on personal experience) that Perle does seem to have insubstantial roots, at least compared to similar family members; and it tends to grow from leaves pretty well, which would be a decent rescue strategy (one I have used myself) when the roots or the lower stem seem to be failing. Leaves are probably not a great solution with a rosette as small as the one in the picture, at least not without sacrificing the last reserves of succulence your plant may have, but they are the route of last resort should you determine the roots or lower stem are rotting.

For what it's worth, Perle is also very good at enduring root loss or water stress (drought), at least up to a point, so be sure not to give up prematurely.

Thanks for the valuable information Donald and Baja!

Will be patient and careful and see how things will turn out