It looks like it was reformulated a few months ago:
I only used the old version, you can find INCI here:
I’ve been using it for years, I like it because it doesn’t dry out at all. When I test a product or ingredient, I wash my face after each use, sometimes several times a day, and I had no problems with this cleanser.
I thought about it because you mentioned that you want the conditioning effect. When rinsing it off, you can feel that the skin is super smooth, and it reminds me of the feeling of rinsing off hair conditioner. After drying, I don’t feel this smoothness very clearly on my face. A bit different than with ingredients such as PCA Glyceryl Oleate or Sucrose Cocoate. They affect the foam in my opinion, but I don’t feel this smoothness while rinsing. In addition, the PCA Glyceryl Oleate irritated my eyes, and the Sucrose Cocoate had a distinct, not so nice coconut smell.
I used Disodium/Sodium Cocoyl Glutamate, but the conditioning effect was much less noticeable, and imperceptible to me when using gum for thickening.
In my little experience, it’s rather hard to create a non-drying product without the use of thickeners. I tried a combination of different surfactants, with and without refatting surfactants, and the amount of surfactants that was enough for cleansing + was non-drying, was not sufficient to thicken even with a lot of salt. I mean, of course after adding salt it was thicker, but just not enough. On the other hand, in some cases if you use a thickener, the foaming and cleansing power is weakened. Then you can try to thicken the product in another way, for example with Sorbithix L-100.