Is zakat obligatory on land held in common throughout the period of waiting to determine the price difference, given that the partner's intention has changed to selling the second plot of land and returning the inquirer's share?

The first plot of land, if purchased for residential building and not for sale, has no zakat (definition) due on it. Similarly, if one partner buys the other's share in it, neither of them owes zakat, because the intention to trade does not convert something into a trade item after its acquisition. Zakat on trade goods is only obligatory under two conditions: actual ownership, such as through purchase, and the intention to trade at the time of acquisition.

As for the second plot of land, which was purchased with the intention of trade, zakat is due on it. If your partner's share in it was sold to you in exchange for your share in the first plot, then zakat becomes obligatory on it if your intention remains commercial and you do not intend to build for yourself. However, the sale is invalid due to the unknown price, as the second plot is more expensive and the price difference was not specified. Therefore, both plots remain under your ownership. There is no zakat on the first plot, and zakat on the second plot is jointly obligatory on both of you.