I’ve found a way to at least work around the issue so that the proxy can be used:

If you load another website first — for example, Wikipedia — before navigating to csfloat.com, it seems to work fine. You can add something like this to your code:

await page.goto("http://wikipedia.com/", {
  waitUntil: "domcontentloaded",
  timeout: 30000,
});

Then, after that, navigate to csfloat. Everything seems to work correctly this way.
Does anyone have an idea why this might be happening?