WieWaldi Currently I can only pedal comfortable without shoes, having the shaft of the big toe on the pedal. Exactly as she described in the video, but with socks. In this position I can rely that the pedal-springs are strong enough to lift my toe up without the need to do it actively by myself. Before that I had a too big portion of my foot on the pedal and was always afraid the weight of my foot is enough to press it down. Therefore I used my muscles to lift the foot instead of just relaxing. Still, I tend to fall back into that habit to actively lift my foot with muscles.
I feel less of a weirdo to see someone else looking at things I had to work out, where it seemed I was the only one to "obsess about details" but that twisted path ultimately helped me. 😃
I highlighted "weight of my foot" because I wondered, how much weight does a foot actually have? If the foot is heavy, could the weight of the leg (or more) be contributing? If one leans slightly forward to play, what holds the shifting weight of the body? The tripod of seat and feet - so the heel of the left foot, and also the right foot. When I was fixing my pedal mechanics, I was partly leaning into the front of my foot - in my case there was a mess to fix.
The pivot point at the ankle also isn't quite where we think. Thomas Mark's "What Every Pianist Should Know about the Body" goes into that on one page - I was quite surprised at the time.
When I was sorting all this out, I did one of my "I've got weird questions" thingies with my teacher. Namely, do we:
(1) expend energy to press the pedal down, and relax for the pedal to push the foot back up
(2) expend energy to raise the foot off the pedal, and let the weight of the foot lower the pedal
(3) a bit of both, depending
The answer: probably either one depending on the pedal of that particular piano.
And when we push the pedal down, maybe some of the impulse does come from the front of the foot (toe area) because the foot isn't just one long clump: its structure is as complex as the hand.