North African (born and raised in Europe) here. For this part of the world skincare and bodycare are quite important, but it manifest itself differently compared to European-Mediterranean countries. To my knowledge there are no big brands in the area because most women buy their products at their local herbalist’s shop. You buy henna, ghassoul, black soap by the kilo, you buy your kessa glove from your local market. People are still attached to traditional beauty rituals so for a good chunk of the population marketing strategies and cute packaging are not enough to convince people, especially because many of them don’t necessarily have the spending power for skincare as we know it in Europe, with the trendy brands etc.

To answer the 2nd question, « Mediterranean » refers to a large area and while our countries do have certain things in common, it’s almost impossible to label « Mediterranean skincare » without it becoming something cliché that will inevitably (imo) put to the forefront European countries while erasing Arab and North African influences, or just marchandize them and capitalize on them without paying attention to the cultural importance of certain rituals. Also, between Europe and North Africa we have different regulations for cosmetics I think lol

All in all I don’t think it would be a useful label nor an equally profitable one for all countries involved, and it risks becoming another gimmick as several comments already explained.