I've never seen another game where you can completely design your own character to be unique.... anybody knows any other games which do so?

By that criteria, The Sims is like toribash

Basically a clone game

Toribash Next

Basically any game with character creation and mods that add more options to pick for the creation.

Sumotori, ragdoll ninja, overgrowth(?)
They're the most similar games to toribash I can think of, as a whole.
Your criteria is odd as it's pretty far from the defining features of the game.
I remember old WWE games being pretty fun in terms of customisation.

When I searched up Toribash related content on YouTube back when I was first starting out I saw a lot of content related to the Endorphin, which is a motion synthesis simulator by Natural Motion. If you like the physics and action aspects of Toribash you might have some fun playing around with it. Although, you would have to find an upload and license key posted somewhere online in order to use it because the project was canned by the developers.

Good god, so far no answers, I've done the same search and came empty handed. There's minecraft as an example of a not.so.good example though, because it's really limited to a low res.
The search is about a game where you can make textures for everyone else to see, games that have steam workshop or are modded offline doesn't count because of the online factor and you can virtually mod textures of any game.

For the next people that answers, at least read the tittle.

Team Fortress 2

skyrim

You can customise your Face in Mount and Blade: Warband.