What role do Sales KPIs play in improving forecast accuracy, especially in unpredictable markets, and what approaches help teams make the most of these metrics?

KPIs can certainly help to improve forecast accuracy. You can even build models to predict an outcome with a high accuracy. Deal velocity, pipeline coverage in different sales stages and forecast categories will help to predict the outcome. The more accurate data is available the better the models will become. This of course is on a pipeline level rather than on the deal level. No model can improve sales execution :-)

This will become more difficult in unpredictable markets of course, however, still possible. Maybe with a higher range of accuracy.