Does the Sa'i become invalid for me if I did not perform the Tawaf of Arrival before the Sa'i, and if it is not invalid, what must I do now?

For the sa'y to be valid, it must follow a tawaf of ritual (either tawaf al-qudum or tawaf al-ifadah). Therefore, if someone performs sa'y without it being preceded by tawaf al-qudum or tawaf al-ifadah, they have omitted a pillar of Hajj, which is the sa'y.

Thus, the person remains in the state of ihram and will not achieve the second tahallul (partial release from ihram) until they perform the sa'y. Consequently, they must refrain from whatever is forbidden for someone in ihram before the second tahallul, and return to Mecca to perform the sa'y.

It is more cautious to repeat the tawaf along with the sa'y, to avoid the dispute of those who stipulate continuity between them. However, if she is unable to come to Mecca and complete the ritual, her ruling is that of someone prevented (from completing Hajj), and she may release herself by offering a sacrificial animal (hady). If she is unable to do so, then by fasting for ten days.