[tialaramex]

As well as SNI which is mentioned in an existing thread, it's possible you were seeing OCSP the Online Certificate Status Protocol. This is particularly likely if the packet was going to a completely different server.

OCSP is a plaintext (the answers are actually signed but they aren't encrypted) protocol to assure your client that the certificate it's looking at hasn't been revoked.

The correct fix for privacy is that OCSP Stapling should be used. Instead of clients fetching OCSP answers and thereby revealing who they're talking to, the server should pre-emptively fetch OCSP answers about its own certificates, and "staple" the latest good answer to its certificate, saying "Look, here's proof my certificate is still good". This stapled answer is then provided to the client, over the encrypted TLS connection, since OCSP is signed the client can trust this stapled answer and needn't fetch it themselves.

DoH servers should definitely have OCSP stapling. I'm sure the big famous ones do.

[aaomidi]

Alternatively we could get shorter lifetime certificates. I hope for a day where ocsp becomes unnecessary because certs are only valid for a day or two.