Flaws in your squat technique will hold you back from progressing. Overhead squats can improve the squatting pattern and should be a regular part of your strength training program.
The overhead squat requires a more upright posture than the back squat and you're forced to execute the squatting pattern precisely, otherwise the bar would drop to the front or back.
Have a look at the video. You can see the high concentration level of the athlete and accurate execution.
Move slowly through 2-3 rounds of 5 reps on each side to prep the shoulder before your next pull-emphasized training day that involves things like pull-ups.