Planck length, mass, time and so on are built from the most fundamental physical constants - the speed of light, the Planck constant and the gravitational const

Planck length, mass, time and so on are built from the most fundamental physical constants - the speed of light, the Planck constant and the gravitational constant - all of which are independent of the reference frame. But I don't think that is actually important. It has more to do with units, i.e. the concrete value of the speed of light is determined by the way we defined the meter and the second and the same holds for the other constants. But that has no physical content, the value 299,792,458 m/s is a historical accident and we could as well have ended up with 42 foo/bar. So what physicist do is just set those constants to one and get rid of those arbitrary numbers by choosing appropriatei units, e.g. the speed of light becomes one lightyear per year. Because nothing moves faster than the speed you can then also go further and measure velocities with a unitless value as a fraction of the speed of light, i.e. a number between zero and one, as it it appears in the equations of special relativity. So if you throw those constants together in relatively simple expressions like hG/c³ you again get one as the numerical value and here for example something with units of area, the Planck area. But there is also no real physical content in the Planck units beyond that. Because the laws of physics usually contain all the constants and values in small powers and with small factor like a Pi here and one half there those units define scales of length, time and so on where the quantities are all about one, nothing is ten to the twenty or minus thirty. So at that scales the laws of physics may show interesting behavior like (1 - v²/c²) becoming zero as v approaches c but that are also more like heuristics than hard truths. So to make a long story short, Planck units are frame independent because they are built from constants and they are nice to think in because many things are of order one - a black hole of one Planck mass has probably a horizon of one Planck area or four Pi Planck areas or something small like that - but they are not that special.