In my mind, what I'm guessing is when I applied Catmull-Clark I created more vertices/edges or something? And there are some unassigned vertices or something. No idea, but when using the model without Catmull-Clark, it works pretty much fine (I mean even before, Valve's models are a bit scuffed, but still way better than what I get). I really need the version with it though, it looks a lot smoother and better. As for the weight paint, I don't know, I am comparing both the old version and the new one and they're literally the same, so I'm not sure if it's from that?. I have no idea how to start on this, so everything is appreciated.
So the biggest difference between your pictures is that in one, the armature is unposed, and in the other, the thighs appear to have been rotated 180 degrees. The solution to that problem is, as the old doctor joke goes, "Don't do that." If you want your model to look good, don't pose the model in poses that a real person could never match. If that picture is from a realistic pose, you'd want to include that pose in the file to demonstrate the issue; I haven't been able to recreate it from your picture (with just a bit of effort.)
Your model does feel a little bit playdough-ey. I can see what you're talking about. In this case, the reason for that are the weights, which feel a little bit diffuse to me-- not sharp enough. You might consider using a weights/smooth operation, on all groups, with a negative expand/contract, and see if that improves your experience of it.
One thing that you may not realize is that you've told Blender to subdivide the model after the armature modifier, but it's very unlikely that SFM has the real-time subdivision that Blender has (because CC subdivision is costly, and so game engines don't do it.) If you're getting any subdivision on your export, it's probably being applied to the model before the armature. Subdividing after an armature is usually preferable for animating purely in Blender, but if you want to get a feel for how it'll look in SFM, you'll want to drag the subdivision modifier up in the stack, to above the armature modifier.
Another thing I notice on this model, that may be contributing to your feelings about it, is that there's quite a bit of volume loss on the joints. You might consider enabling "volume preservation" on the armature modifier-- but then again, you might not, as this might not be something supported by SFM (the game engine will be doing the deformation, and only in ways that it knows how.) There are some ways to change the "topology" of a model to better hold the shape at the joints that don't require this, and you might consider researching joint topology. You might also consider "corrective shapekeys", assuming shapekeys are supported by SFM.