Around 30 minutes later I went on facebook.com, and saw an ad to this specific service.

Some context which I think controls for "simpler" explanations to this co-occurrence: I did not go on this service's website following our chat, nor did I search for it on Google. I did open the service's app on my phone, but it was already installed and as far as I know (and hope) Apple does not share this kind of usage data, let alone with Facebook.

WhatsApp chats are encrypted end-to end. My buest guess is that Facebook is able to do some kind of homomorphic encryption, which it was claimed to be able/trying to do [1,2].

[1] https://www.macrumors.com/2021/08/03/facebook-researching-analyzing-encrypted-data/

[2] https://www.androidauthority.com/whatsapp-encryption-ads-2728774/