Well, what this indicates to me personally is not a knee problem at all. Tingly, pins and needles kind of feeling is usually one thing and one thing only: nerve-y junk. Given that this isn't really "pain", you say this feeling worsens when you stand and when you bench press or OHP but goes away when you sit or squat. What this indicates to me is the following:
In my opinion it is likely your hips or low back is out more than a knee. I suppose it could also be a femoral alignment issue pressing on the sciatic nerve as well in certain positions. But you
get extension based tingly "pain" and
do NOT get flexion based tingly pain and
are able to function normally in pretty much all ways with no major issues.
To me this says that something is impinging or pressing on a nerve somewhere when your spine is extended, specifically lumbar region of the spine. Standing is more extension than sitting, especially as most people sit slouched or hunched over, and overhead pressing is very extended for most people. Benching more extended still. You are bracing the spine hard in the squat, probably keeping it more neutral than arched, which is probably the genesis of your feeling good/tingle free in the squat
The trick is the other "not quite 1 'something' else" you feel. My intuition says the knee itself doesn't need much except some time away from super heavy squats...like say for single leg work. And you need to prioritize ab work, both flexion and anti-extension (plank, ab roll outs) for a while in both frequency and volume, but I would give the overall priority to anti-extension. You also need to seriously strengthen your glutes, AND your glute medius (the outside of the hip, that X band walks make burn). This I agree with. I also think you may just benefit from stretching the hip flexors as well since they may be playing a part in the fiasco. The warning here would be to keep your low back absolutely flat while you stretch them, so that involves bracing the abs and glutes hard as well during the hip flexor stretches.
You might very well benefit from a chiropractor appointment. If it's just a misalignment caused by the wild squat it probably can be fixed with an adjustment. I would still hammer away at these things though, so that the adjustment isn't pissing into the wind.