Figura VS ViaVersion

There is a mod that adds exactly that, and it's free. https://github.com/Blancworks/Figura

Third thing: Compatibility for other skinning mods. Things like capes and deadmau5 ears should be able to be textured in HD. The primary support should be for OptiFine capes, but that can be extended to other mods once OptiFine support is complete. One mod I think should really get support is Figura.

There sure is! There’s a new client side mode called Figura. It works on vanilla servers. https://github.com/TheOneTrueZandra/Figura

The mod can be found here: https://github.com/TheOneTrueZandra/Figura

From the other post

currently, you have to attach stuff to model parts https://github.com/TheOneTrueZandra/Figura/wiki/Blockbench-Keywords

Lua scripts are optional. You can look over https://github.com/TheOneTrueZandra/Figura/wiki/Creating-a-basic-avatar#viewing

ViaVersion: Download ViaVersion

ViaVersion: ViaVersion is a plugin that allows players to join your server with newer or older versions of Minecraft. It supports most features and protocols from 1.7 to 1.20.1. You can download ViaVersion from here and join their Discord for support here.

I think the only way to totally accomplish what you're trying to do would be with a server rather than a realm. You could run a 1.16 server with ViaVersion to allow newer versions of Minecraft to connect to it. I believe that this would maintain 1.16 world generation even when generating new chunks.

Okay turns out there IS a mod that seems to do exactly this. I haven't taken a close look at this yet but this seems like it would do what you want. https://github.com/ViaVersion/ViaVersion

https://github.com/ViaVersion/ViaVersion.