What are the consequences for my wife who was unable to perform Sa'y of Hajj due to lack of time and exhaustion, and is it permissible for me as her husband to approach her, knowing what has been mentioned, and what are the consequences for me if I have intercourse with her?

If your wife performed Hajj as a Mutamatti'ah, Qarinah, or Mufradah, and she did not perform Sa'i between Safa and Marwah, then she has not completed the second stage of tahallul (exiting the state of ihram). She remains in her state of ihram with regard to intimacy and its preliminaries, because Sa'i is a pillar of Hajj.

She must go to Makkah to perform Sa'i, and it is not permissible for you to be intimate with her until she completes tahallul. It is safer for her to repeat the tawaf along with the sa'i, to avoid the dispute of those who stipulate continuity [between tawaf and sa'i].

If she is unable to go to Makkah and complete the ritual, then her ruling is that of one who is prevented (muhsar): she exits ihram by sacrificing an animal, and if she is unable to do so, then by fasting ten days. As for any intimacy that occurred out of ignorance, there is no penalty for it.