How is Zakat calculated for land sold partially for money and partially for real estate, while a portion of it remains, given that the sale is recent and the time for Zakat is before Eid al-Adha?

There is no zakat due on the land that was not intended for trade when it was acquired, nor on what has been sold from it now. Rather, the proceeds from the sale should be held for a new hawl (lunar year), and if they reach the nisab (minimum threshold) and a hawl passes over them, then zakat is due.

Similarly, zakat is not obligatory on real estate purchased with the price of the land unless it was intended for trade. However, if you rent it out, then its rental income is subject to zakat if a hawl passes over it and it reaches the nisab.