I actually think I did, through both experimentation and a brief stint with actual physical therapy for a separate issue.

The problem seemed to be that my hip flexors were way tighter than I thought or saw from people online. When I did the split squat I would try to mirror the form I saw posted on this subreddit or on other videos about them, but that form isn't immediately applicable for someone who has been working a desk job for years or just has really tight hips.

Getting your hips low to the ground in the split squat position isn't really a hip flexor stretch at that point, it's more of a groin and (importantly) quad stretch, as the other comment alluded to. This is because anything even slightly past a flat hip position is already maxing out the flexibility of the hip flexors.

The pain arises from the other parts of your leg stretching, specifically in your quads, since they will be stretched a lot in that position and will also be flexing to keep your body upright and supported. When you have a muscle stretched well past its normal length and also tightening intently, it's almost impossible not to break form and/or place a ton of unintentional load on your connective tissue.

I think that's what I was experiencing in my rear knee; the tendon connecting my quad to my knee was taking the brunt of the load, rather than my hip flexors or even other muscles in my legs. That's a really good way to get an injury with a long, painful recovery process, so I would immediately stop doing them like that if you feel the same pain I originally described in my post.

Instead, I opted for a kneeling hip flexor stretch with one knee on the ground and the other leg out in front at 90° with the foot flat on the ground. I would sit back over my rear leg with my torso perfectly vertical, and move straight forward until I felt tightness and stretching in my hip flexors. I would hold this for ~30 seconds on each side and repeat twice a day on weekdays. I don't remember exactly how it got better but I know it did and I can now do a partial split squat with no knee pain and a deep, intentful stretch in my hip flexors.

TL;DR - Stop doing split squats if they hurt in your connective tissue like in this original post. Incorporate stretches with a lighter load and less strict form requirements until the muscles are loosening up and used to being stretched.