The claim that “screen time directly leads to obesity and diabetes” is very misleading. To answer this question you have to define “direct” in this context. A direct outcome of something would mean that by doing something (screen time), that itself makes something else happen (obesity, and diabetes). Screen time itself doesn't make you obese or give you diabetes. But a lot of screen time can lead you to spending a lot of time in one place, potentially leading to obesity.
There are a lot of sources that verify the fact that obesity is a lead outcome of screen media exposure. Ex. PMC. But not one of them say obesity and diabetes is a direct outcome of screen time.