Is anyone aware of a UI component library for compose multi platform (ideally supporting web targets / not using AWT), or one that is for Android but has support for large screens in mind?

What is missing in the Material components for you right now?

It's just that the Material design system seems to have a rather heavy priority for smaller screens, at least to me, what do you think?

I’d say you need to be more specific in terms of what you’re looking for. Are you missing components that specifically target larger screens, such as side sheet, or multi-level drop down menus, or maybe something else? Or maybe you’re looking for components that work better with non-touch interfaces such as mouse, keyboard, stylus or joystick? Or maybe something else?