I appreciate it isn't central to the article's purpose, but this is wrong, and as background noise it contributes to a misunderstanding that causes other problems every time it occurs.
I will describe what's done in TLS 1.3 because that's clearer, but you should know this isn't how your TLS 1.2 server actually works in real use today either.
TLS encryption doesn't care about these certificates. (Elliptic curve) Diffie-Hellman is used to agree random keys, and the random keys encrypt everything. In TLS 1.3 nobody even says anything about certificates before that step happens - the certificates are sent encrypted.
So why have certificates at all? Because without them you're having a secure conversation... but you don't know who you are having a conversation with. So now we're definitely communicating securely with someone let's check it's who we expected. In TLS 1.3 the server (and optionally client) can send a certificate, claiming some identity, and then they sign the transcript (a record of everything said so far) with the corresponding private key, in effect saying "This is proof you are having this conversation with me".