A simple mod for Minecraft 1.19.4, 1.20.4/6 & 1.21 (Other versions are not tested).
The configure screen requires Cloth Config and Mod Menu to open (or you can edit the configuration file manually).

For some reason, some minecraft servers (especially 1.19.3) won't send you your skin parts if you enter another dimension, and it makes your skin looks ugly.

With this mod, your skin layers will always be shown (Following the client's skin options).
And it will automatically resend your client's options in order to enable your skin layers to be seen to others (Configurable).
If other players still cannot see your skin layers, you can simply press N to refresh your skin parts manually.

This mod doesn't seem work well with 3d-Skin-Layers, so please disable it first and try again before reporting bugs if it's installed.

To compile on *nix operating systems, run:

chmod +x gradlew
./gradlew build

For Windows, run:

gradlew build

Then, the mod jar file will be located at fabricWrapper/build/libs/ShowMySkinParts-{VERSION}-all.jar.