Assuming you sell the property as a single lot and are not splitting the property, then:
Remember that "real property" is land, plus anything that is permanently attached. You bought the land and you plan to sell the land (along with structures, trees, shrubs, utility services, and anything else that happens to be attached to the land. You don't allocate costs between the different structures on the land unless you are dividing the land into multiple lots and selling them separately. All your adjustments to basis (increases for improvements and decreases for business use) happen to the land.
Your cost basis is the original cost ($125,000) plus the cost of improvements ($125,000) minus depreciation.
If you want to divide the land into separate lots and sell the ADU on its own lot without selling the main home, that will indeed be more complicated and may require professional review.
