Use API for Facebook check in faucet

[ligi]

Rationale

follow up of #22137
In the future crawling might also break for mobile as it did for the normal site.
Being proactive here instead of reactionary could prevent users running into this wen it happens

[holiman]

If we add a couple of testcases like these, we'll notice when they break it for us: #22137 (comment)

[holiman]

Faucet is long gone