The issue you're having is that in the default model set the base of the extended piston is shared between both the normal and sticky pistons, while the arm is its own model for each. Because default is the same for both, the designers at Mojang just reused assets in order to save on space.
The solution to this is to create a duplicate of the piston base and give it a different name. Edit that model to point to the sticky textures instead of the normal ones. Then edit the relevant blockstate file for the extended sticky piston to point to your model instead of the one it shares with the normal piston.
I don't have exact file names in front of me, nor examples, but hopefully this description gives you a pretty good idea of what to do.
I'm having trouble changing the textures of the Extended Sticky Piston Model, without changing those of the Extended Normal Piston's Model.
* For me, when a sticky piston is extended, the piston's head has my custom sticky textures, but the base uses the normal piston's textures.
JSON Files:
piston_extended
The issue you're having is that in the default model set the base of the extended piston is shared between both the normal and sticky pistons, while the arm is its own model for each. Because default is the same for both, the designers at Mojang just reused assets in order to save on space.
The solution to this is to create a duplicate of the piston base and give it a different name. Edit that model to point to the sticky textures instead of the normal ones. Then edit the relevant blockstate file for the extended sticky piston to point to your model instead of the one it shares with the normal piston.
I don't have exact file names in front of me, nor examples, but hopefully this description gives you a pretty good idea of what to do.
That had done it. Thank you, Sir!
EDIT: I'm now trying to do something similar to hoppers. The texture should become more solidified, when disabled/locked.