Two more things that change how you look more than a camera upgrade would, both free.
Camera height. Put the lens at or slightly above eye level. A laptop on a desk shoots up your nose, and no amount of resolution rescues that. Books under the laptop, or raise the external camera on something. This is probably the single most noticeable improvement per second of effort available.
Distance and background. Sit far enough back that you are not filling the frame, and have something with a bit of depth behind you rather than a wall thirty centimetres away. Depth reads as three-dimensional; a close flat wall reads as a passport photo.
And two settings worth checking on the camera you already bought, since a lot of them ship badly configured:
Turn off any automatic beautifying or scene modes, which frequently produce the soft flat look people blame on the sensor.
Lock the exposure and white balance if the software allows it. Auto exposure hunting as you move is a large part of why calls look unstable, and auto white balance shifting between your lamp and the window is where the grey comes from.
Do the light, the height and those two settings, and the camera you have will look like a different camera.