Animations in the Animator not running in-game.

Hello,

I’m new to Unity, and running into an issue.
I was already following a couple of tutorials, but looks like there’s an issue i cannot fix after hours spent on it:

My character (an animated rat purchased on the Asset Store) has an animator controller with the different animations that are set properly with transitions and parameters.
But in-game, the animations don’t run.
As you can see on the provided screenshot, the animations run in the Animator, but not in-game.
I tried to switch between different default animations, parameters, and variables. None of the animations are working in-game.

However, when I put, say the Rat_Walk animation, as an Animation Clip on the Player, the provided animation plays in-game. But that’s not what I need.

What did I miss?

I just found out there’s no Motion (on the right), and I cannot set it to any of the Rat animations.
I can set it to any other animation though. Even the Take 001 animation that came with the rat, which is grouping all 5 rat animations.
If I set this one, then it works, but playing the Take 001 clip, not the individual ones. Still not what is wanted here.

So, would this issue be related to the animations themselves?
How to fix it?