How to use Minecraft item textures variants in java?

Regarding the Minecraft item textures, you can use the CustomModelData nbt tag. In the .json file of the model you are editing, include one or more override models. Example:

{
  "parent": "item/handheld",
  "textures": {
    "layer0": "item/carrot_on_a_stick"
  },
  "overrides": [
    { "predicate": { "custom_model_data": 1}, "model": "item/carrot_on_a_stick/1" },
    { "predicate": { "custom_model_data": 2}, "model": "item/carrot_on_a_stick/2" }
  ]
}

This is an example where the texture of a carrot on a stick is changed. This is replacing the normal text in the carrot_on_a_stick.json . The models being accessed are in a folder next to carrot_on_a_stick.json called carrot_on_a_stick . The models are respectively called 1.json and 2.json.

You'll probably want to have some knowledge of Minecrafts json modelling. For that, I recommend this site. To give yourself one of the custom-textured items in-game, use /give @s minecraft:{CustomModelData:}.