[routine help] [product question] - Should face skin feel good after cleansing *without* needing to apply anything after?

I hope my question makes sense. I'm referring to the face (but if this applies to body too, feel free to mention). I will apply moisturizer in everyday life regardless of the answer to this. My question is more theoretical.

Is it a good "test" of whether your cleanser is good - to see how it feels without having added any moisturizer?

I have normal skin that feels slightly dehydrated (not dry) after using a gentle cleanser or moisturizing soap. So of course if I use a multi-purpose cleanser that's more abrasive, it feels even more dehydrated.

However, because my skin can handle any ingredient, if I use the multi-purpose cleanser and apply lotion/serum immediately after, I find my skin looks overall better (probably because of all the extra ingredients). Not sure if it looking better = healthier or not.

So I've used both gentle cleansers and multi-purpose cleansers in the past and have a slight preference for the results of the multi-purpose ones. But I'm not sure if it's best practice.

TL;DR - (not a question about moisturizer - I will use it regardless)

Sans any moisturizer, my skin gets slightly tight/dehydrated from gentle cleanser and even moreso from abrasive/multi-purpose cleanser. Does that mean I should stick with the gentle cleanser?

I have a slight preference for the multi-purpose cleansers. But if that's only because of the moisturizer after, does that mean it's stripping my skin barrier too much?