Praise be to Allah.
Tawaaf al-ifaadah and the sa‘i of Hajj are two of the pillars or essential parts of Hajj, without which Hajj is not complete.
If someone does Hajj but he does not do tawaf al-ifaadah or sa‘i, and he completed the first stage of exiting ihram by stoning the Jamaraat and shaving his head, then only intimacy with women remains prohibited for him, and he must go back to Makkah and do tawaf and sa‘i, no matter how long a period of time has elapsed.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Tawaf al-ifaadah is one of the pillars or essential parts of Hajj, without which Hajj is not complete. If someone failed to do it, then his Hajj is not complete, and he must do it. So he must go back, even from his country, and do tawaf al-ifaadah.
In this case, as he did not do tawaf, it is not permissible for him to be intimate with his wife, because he has not completed the second stage of exiting ihram; the second stage of exiting ihram is not complete until after doing tawaf al-ifaadah and sa‘i, if he was doing tamattu‘ [Hajj and ‘umrah together, exiting ihram in between]; or if he was doing qiraan [Hajj and ‘umrah together, without exiting ihram in between] or ifraad [Hajj on its own], and he did not do sa‘i with tawaf al-qudoom [the tawaf of arrival].
End quote from Fataawa Arkaan al-Islam (p. 541).
Shaykh Ibn Baaz (may Allah have mercy on him) was asked: I am one of the residents of Makkah. I did Hajj last year and I did tawaf, but I did not do sa‘i. what is the ruling?
He replied: You must do sa‘i. This was an error on your part, because sa‘i is essential, whether you are one of the residents of Makkah or otherwise. Sa‘i must be done after tawaf; after you come back from ‘Arafaat you should do tawaf and sa‘i. The one who failed to do sa‘i must do sa‘i now.
End quote from Fataawa ash-Shaykh Ibn Baaz (17/341).
If this person did ‘umrah several times after his Hajj, then the first ‘umrah he did completed his Hajj, as the tawaf and sa‘i that he did in ‘umrah made up for the tawaf and sa‘i of his Hajj. It does not matter that he intended that to be for ‘umrah, because he was still in the state of ihram for Hajj, and his entering ihram for ‘umrah is not to be counted. In the case of tawaf and sa‘i, it is not stipulated that there be a specific intention (niyyah) regarding them, intending that they be for Hajj or for ‘umrah, according to the correct scholarly view. See: ash-Sharh al-Mumti‘ (7/403).
For more information, please see the answer to question no. 273955, in which it states that tawaf in a later ‘umrah completes the previous ‘umrah.
Conclusion: the tawaf and sa‘i of the ‘umrah that was done after Hajj complete the Hajj, and the questioner does not have to go back again to do the tawaf and sa‘i of Hajj.
This questioner must sacrifice a sheep, to be slaughtered in Makkah and the meat distributed to the poor there, because he failed to do the farewell tawaf, as doing the farewell tawaf before completing the rituals does not count.
He should beware of waswasah (whispers from the Shaytaan), because it is a disease and an evil. The best remedy for it is to ignore it and pay no attention to it.
See the answer to question no. 39684.
And Allah knows best.