For external-facing APIs and libraries, one reason I've found motivating to write documentation first is that you can "playtest" very quickly as a user/dev who

For external-facing APIs and libraries, one reason I've found motivating to write documentation first is that you can "playtest" very quickly as a user/dev who comes in and starts wanting to use your thing. If you (or another teammate) have to write a use-case snippet of code similar to how you want your thing to be used, based on your docs, you often find friction points and inconsistencies that should be streamlined and simplified. It allows you to start iterating much faster than having to wait until you have a functioning product. It also often lets you avoid sunk cost fallacies where you run into that friction point later but don't want to go back and rewrite/redesign code to streamline the friction point.