I swear I could have made the same post right now. I started a new (completely remote) role recently and I'm feeling exactly the same. I set up meetings with my team members, got to know everyone, tried to take initiative, and asked for small tasks to get up to speed.
But they haven't given me any work and have left me by myself rather aimlessly. I am trying to learn as much as I can and develop context but there's only so much you can do. Being remote isn't helping either. I have no one to talk to really and it's pretty isolating. In an office, ramping up is much faster because you're always in the thick of things.
Ignore the haters on this thread. I'm planning to have a meeting with my manager next week where I will share my progress and ask for the first project I can take up - no matter how small. I have a couple of ideas myself for tasks I can take up.
I would suggest something similar for you if it works. I don't think we should be worried about our jobs, but yeah this doesn't seem very normal to me. I hope we're not in the same company lol.