Owned classic skins that are unavailable to new players, no longer show in Classic Skins as an owner, Although the skin from affected skin-pack loads, you cannot choose that skin again unless via a workaround.

Since every players have different library, reproducing the issue as a player might be impossible, as it requires owning a skin-pack before it was made unavailable to be purchased to others who did not bought that in the first place.

Most notable skin-pack for me were Minecraft Legacy Skin-pack, Dungeons Hero Skinpack, Minecraft X Puma: Sprint Dash and Minecraft x Burberry: Freedom to Go, which are currently unavailable to be purchased in recent days (based by searching on my owned content in Marketplace Catalog).

Workarounds: in the game menu, go to Marketplace (Minecraft Store on PlayStation), and then go to My Library, and filtering the library by Skins or Mash-up. There you can apply skins from owned skin-packs that would not be available if not purchased, this currently does not apply to skins from Super Mario Mash-up Pack on Nintendo Switch as it is not listed on Marketplace Library.

If created as custom character, Switch to Classic Skins by pressing it's icon, then return to Dressing Room, and press "Change Skin" after that as pressing Classic Skin again goes to broken UI.