Yeah, very few really strong people don't train a sore muscle lol. Punisher's on point.
If it's sore, like you can move fine and are a little tender, train. If it's sore like it's significantly stiff AND sore, train but warm-up much more thoroughly and play intensity by ear. If you can't move the muscle, probably don't train it lol. Or just confine your "training" to getting full range of motion.
Honestly, increased frequency is a way to alleviate soreness. Squatting daily (like an olympic lifter would) there comes a point when you just stop feeling sore. To get there you have to go through killer agony...but it happens.
Soreness in general is not a gauge of progress or quality of a workout. It can be a secondary or a tertiary measure, but not a prime measure. This is because any change you make in your routine at all can lead to increased soreness. Go from high rep to low rep 3's? Get way more sore than you were before. Go the reverse direction from powerlifter to bodybuilder? Get way more sore. Run sprints on a track and haven't done it in a while? Prepare to be debilitated. It's really just a sign of change.
Performance in numbers as you mentioned is far superior in terms of assessing progress.
Your body likes to lie to you. I have set a lot of my PR's on days I entered the gym feeling like I was hit by a truck and/or sick and/or dehydrated. So have a lot of people I've known.
There's a balance between listening to your body in the gym to avoid injury (good) and always holding back or never pushing yourself hard enough to adapt (bad).