We study a class of high-frequency path functionals of diffusions with a singular threshold, including the case of sticky-reflection. The functionals are built upon a test function and a normalizing sequence. We prove convergence to the local time, advancing existing results on sticky, oscillating (regime-switching), and skew or reflecting diffusions. Notably, we consider any normalizing sequence that diverges slower than the observation frequency. Additionally, we allow for jointly sticky-oscillating-skew thresholds. Combining these findings with an approximation of the occupation time, we propose consistent estimators for skewness and stickiness parameters.