I'm no expert. I probably know too little about the propagation speed of a wave to understand what you mean there.

But here is a scenario where something is faster than light in the given medium: https://en.wikipedia.org/wiki/Cherenkov_radiation

As I understand, neutrons and gravitational waves are also bound by the speed of causality, because they have no mass. And I believe, unlike light, they are unaffected by electromagnetic forces that a material exerts, so they would presumably (always?) travel faster than light in that medium.

I will also say, that from what little I understand of this video: https://www.pbs.org/video/pbs-space-time-speed-light-not-about-light/
...it sounds like trying to determine the speed of causality by measuring it, is kind of backwards. You're at best experimentally confirming what has to be a given under our laws of physics.

Yes, it's derived from 4 physical constants including c

Its more related to limits of knowability of events beyond a certain scale. Its easy an intuitive to think of it like spacetime is quantized like pixels on a grid with a minimum action requirement of time and energy to move between them. But its not that simple or at least that kind of granular discreteness is not proven (though there are digital physics frameworks that treat spacetime discrete like this)

The Planck length does not define the minimum distance something can move but rather the minimum scale of meaningful measurement that can make a bit of distinction between two microsstates of information. In essence it says that if theres two continuous computational paths that differ by less than a sub-plancks worth of distinction there is no measurable distinction difference between them and the paths get blurred together.

Its a precision limit that defines how exact we can measure interactions that happen within the distance between two points.

It's possible that spacetime is continuous at a fundamental level, but the Planck length represents the scale at which quantum fluctuations of spacetime itself become so violent that the concepts of a 'path' or a 'distance' can no longer be defined in the classical sense, effectively creating discrete quantized limits for measurement precision.

Ultimately this precision bound limit is related to energy cost to actualize a measurement from a superposition and the exponetial increase in energy needed to overcome uncertainty principle at smaller and smaller scales. The energy required to actualize a meaningful state from a sub-planck length would be enough to create a kugelblitz black hole made from pure condensed energy.

This same logic applies to time, giving us the Planck time, the shortest meaningful interval. So, in a way, the Planck scale does define a fundamental limit on the 'speed' at which distinguishable events can occur.