I am not saying there is nothing to this, but this is just a catchy concept with a convincing narrative. The sources are news articles and YouTube videos, not scientific papers specifically addressing the issues mentioned, for example showing a link between self-censorship and online monitoring or quantifying that effect.
The website does link to a lot of scientific studies actually. Both throughout the page and at the bottom.
But I purposefully didn't want to link directly to the PDF's of those studies too much. By pointing to accessible news articles about those studies in the "further reading" section I was hoping to keep things accessible to a wider audience.
Catchy concepts and convincing narratives sometimes precede more rigorous studies. As you yourself cautiously indicated, there might be something to this.
I can't satisfy anyone's need for a thorough scientific paper offhand, but I can certainly add anecdotal evidence : I regularly self censor online precisely because I know I'm being tracked in some fashion (and probably in ways I haven't even thought of : retroactive big data analysis 20 years from now is likely to be more sophisticated than it is today). I doubt I'm the only one.