Did the actions of the four Rightly Guided Caliphs count as part of the Sunnah?

The questioner:
He says: Honorable Shaykh, may Allah grant you success. He says: You mentioned, may Allah preserve you, in a previous lesson that the second adhan on Friday is part of the Sunnah and not an innovation. He says: Is the Sunnah only what the Messenger (peace and blessings be upon him) did? Or is it what the Messenger (peace and blessings be upon him) did, as well as what the Companions did?

The Shaykh:
What the Messenger (peace and blessings be upon him) did, that is the Sunnah, and so on.

The questioner:
And that is what the Caliphs did, not all the Companions.

The Shaykh:
The four Rightly Guided Caliphs. This is part of the Sunnah of the Messenger (peace and blessings be upon him). “Hold fast to my Sunnah and the Sunnah of the Rightly Guided Caliphs who came after me,” by way of… meaning the four. Yes. And the first adhan on Friday, this was ordered by 'Uthman ibn 'Affan (may Allah be pleased with him), the third Caliph. Yes. So it is part of the Sunnah of the Messenger. Yes.