The Ready State Virtual Mobility Coach is like having a virtual Kelly Starrett in your pocket.
Single leg deadlifts CAN be a good choice to help with this, but their effectiveness in actually getting your glute medius to do its thing and pattern that into your movement is going to be dependent on you making sure the stance limb is stable and not collapsing inwards. If I perform a single leg deadlift and my foot collapses and my knee drifts inward, I miss my chance to pattern that hip stability (the glute med stuff) into the movement.
The movement cues related to lower body ER torque (“screw your feet into the floor”, “knees out”) are going to be important points of focus. Using a looped piece of theraband or a light resistance band above the knees during air squats can give you a bit of extra tactile cuing for shoving the knees out, but just going through the motions won’t be enough. You need to approach those air squats with the same intent you would apply to a big PR attempt and WORK against that band. Try a set with the band, a set without the band. Go back and forth for a bit, working to apply what you learned in the banded sets to the naked sets.
This muscle is basically missing it’s cue to fire in sequence when you’re moving, and it will probably take some consistent attention and a step back to some really basic movements to deal with it.