It’s a bit like the chicken and the egg: did inceldom turned them into right-wing white supremacist misogynists or were they already that way?

It's the opposite, white supremacy turned them into incels.

The vast majority of "forever alone" men don't commit shooting sprees or even consider doing so.
A disproportionate majority of incel shooters are also white.

White culture/history tells white men that they are omniscient, all powerful, etc. White men internalize this. The bottom-of-the-barrel men start to see this white privilege inevitably slip away, and it radicalizes them because they feel a sense of loss. They grew up thinking they were up 50 points, but in actuality they were only up 5.