Yes you should know how to model, even if you use pre-made assets you should be able to modify them the way you want, since it’s rarely a perfect match, and each project has always very precise needs.
As for what to learn, if you’re new to 3D I suggest you learn a bit of everything first, don’t focus too much on modeling for video-game but try to learn a bit of everything to a point you start to make good looking stuff without help from tutorials. Knowing a bit of lighting, animation, rig at least to a very basic level will always be helpful even for a modeler.
And once you have that basic , broad, knowledge you can start to focus on specializing and if being a 3D modeler for video game is still your thing then go for it.
To sum up really quickly, some people works for small companies therefore small projects but they’ll be able to touch a lot of different things ( small teams).
Big companies looks for people much more specialized.
As for modeling some artist specialize in characters / organic modeling, then they should know digital sculpting, anatomy, and a few other things.
Next to that, there is hard surface modeling, if you like to model robots, weapons, vehicles, then it’s different tools that are used and obviously anatomy knowledge won’t help you there
You can also be an environment artist, which is a bit different from these 2.
But none of this is really important in the beginning and it’s great to try a bit of everything first, it will strengthen your skills !