Is the Hajj valid given that the Tawaf and Sa'i were performed with the intention of Umrah due to ignorance that they were for Hajj?

The Ifrad (definition) Hajj is for one who intends Hajj alone, without performing Umrah (definition) before it. Upon reaching Makkah, they perform the Arrival Tawaf (definition), which is a Sunnah (definition). They may then perform the Sa'y after it, and this will suffice for the Hajj Sa'y. If the person performing Ifrad intends Umrah while already in a state of Ihram (definition) for Hajj, their Ihram for Hajj remains valid, and the inclusion of the intention for Umrah does not affect it. However, if they have exited the state of Ihram after the Tawaf and Sa'y (by shortening or shaving the hair), their Ihram has transformed into Umrah. In this case, it is recommended for the person performing Ifrad to change their intention to Umrah if they have not brought a sacrificial animal (Hady). Then, they would enter into Ihram for Hajj on the Day of Tarwiyah (8th of Dhul-Hijjah), thereby becoming a Mutamatti' (one performing Tamattu' Hajj) and owing the Tamattu' sacrifice. Your Hajj is valid in both cases, whether as Ifrad or Tamattu'.