Should I use that the paid/adjusted in 2025 for 2024 number on my 1099-INT "Detail Information of Dividends and Distributions" for the adjustment amount?

not sure if you mean 1099-INT or DIV but either way there should be a 1099 summary with totals in all the boxes which is what you should report, the paid/adjusted detail should just be giving you detail for the total already reported in the 1099 boxes.  Check the totals vs. what is reported in the detail to confirm but you likely don't need to adjust anything further on the 1099 for this.

Generally, a common adjustment to a 1099-INT is for accrued interest paid on bonds.  For 1099-DIV the most common manual entry is to specify the US Government Obligations $ amount for state exemption.