Can you explain? I do understand ECDH, and therefore how the two parties can agree a shared secret even if their communication is public. But I feel like I'm missing some details here

If Alice pays Bob via a silent payment, does Bob need to know that Alice specifically might be sending him an SP? Or can he easily just scan the blockchain for payments to him regardless of the source?

I guess the answer is here in this 'Scanning' section?: https://github.com/bitcoin/bips/blob/master/bip-0352.mediawiki#scanning