When playing on multiplayer worlds my friends can't see my classic skin even I see it. They see me as Steve or Alex. They also can't see my player picture on pause menu. It appeared a few months ago before the release date of 1.20. I tried to reinstall the game, to resign in and I also verified if the skin does not have any problem. Later I understood that it happens with all classic skins. I tried to use a simple custom skin edited in Minecraft app. I saw that they can see it.

Conclusion: Other players can't see my classic skin even I see it.