Bought a much better webcam and I look exactly as bad as before - is it the lighting rather than the camera?

The cheapest version that genuinely works, and it is much less than the videos suggest.

One light, in front of you, slightly to one side, above eye level, pointing at your face. That is the whole thing. Not beside the monitor pointing at the wall, at you.

What to use, in ascending cost:

A lamp you already own, moved. Free. Take the shade off or aim it at a wall or ceiling near you to soften it.

A sheet of white paper or card propped on the desk to bounce light back into the shadow side. Sounds absurd, works, costs nothing.

A cheap LED panel or ring light on a stand or clamp. Genuinely fine at the budget end for this purpose.

Slightly to one side matters - light straight on is flat and unflattering, and light from one side gives shape. Above eye level matters because light from below is the horror-film angle.

Then deal with the window. Either close the blind when it is behind you, or turn the desk so the window is in front of you or to the side. If you can face a window during the day, that is the best free light there is and you may not need a lamp at all.

Total cost for most people: nothing, or the price of a small panel.

You bought the second thing first. Light matters more than the camera, and it is not close.

A camera sensor needs light. Given plenty of it, even a modest sensor produces a clean, colourful picture. Given little, every sensor amplifies what it has, and amplification is where the grain and the flat grey come from. That is why your new camera looks the same, it is doing the same amplifying, slightly better.

Your specific symptoms map exactly:

Flat and greyish - a ceiling light directly above you. It lights the top of your head and leaves your face in its own shadow, with no direction at all.

Grainy, not enough light reaching the sensor, so the gain goes up.

Worse for half the day - the window behind you. The camera exposes for the bright background and leaves your face dark, and there is nothing a camera can do about being pointed at a light source.

The order of operations that actually works: light, then background, then camera, then microphone quality. Most people do it in reverse and are disappointed at every step, which is exactly the experience you have had.

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.