The Planck units are bogus units that do not have any significance.
Perhaps our theories of time and space would break down at some extremely small scale, but for now there is no evidence about this and nobody has any idea which that scale may be.
In the 19th century, both George Johnstone Stoney and Max Planck have made the same mistake. Each of them has computed for the first time some universal constants, Stoney has computed the elementary electric charge in 1874 and Planck has computed the 2 constants that are now named "Boltzmann's constant" and "Planck's constant", in several variants, in 1899, 1900 and 1901. (Ludwig Boltzmann had predicted the existence of the constant that bears his name, but he never used it for anything and he did not compute its value.)
Both of them have realized that new universal constants allow the use of additional natural units in the system of fundamental units of measurement and they have attempted to exploit their findings for this purpose.
However both have bet on the wrong horse. Before them, James Clerk Maxwell had proposed two alternatives for choosing a good unit of mass. The first was to choose as the unit of mass the mass of some molecule. The second was to give an exact value to the Newtonian constant of gravity. The first Maxwell proposal was good and when analyzed at the revision of SI from 2018 it was only very slightly worse than the final choice (which preferred to use two properties of the photons, instead of choosing an arbitrary molecule besides using one property of the photons).
The second Maxwell proposal was extremely bad, though to be fair it was difficult for Maxwell to predict that during the next century the precision of measuring many quantities will increase by many orders of magnitude, while the precision of measuring the Newtonian constant of gravity will be improved only barely, in comparison with the others.
Both Stoney and Planck have chosen to base their proposals for systems of fundamental units on the second Maxwell variant, and this mistake made their systems completely impractical. The value of Newton's constant has a huge uncertainty in comparison with the other universal constants. Declaring its value as exact does not make that uncertainty disappear, but it moves the uncertainty into the values of almost all other physical quantities.
The consequence is that if using the systems of fundamental units of George Johnstone Stoney or of Max Planck, almost no absolute value of any quantity can be known accurately. Only the ratios between two quantities of the same kind and the velocities can be known accurately.
Thus the Max Planck system of units is a historical curiosity that is irrelevant for practice. The right way to use Planck's constant in a system of units has become possible only 60 years later, when the Josephson effect was predicted in 1962, and SI has been modified to use it only after other 60 years, in 2019.
The units of measurement that are chosen to be fundamental do not matter in any way upon the validity of physical laws at different scales. Even if the Planck units were practical, that would give no information about the structure of space and time. The definition of the Planck units is based on continuous models for time, space and forces.
Every now and then there are texts in the popular literature that mention the Planck units as they would have some special meaning. All such texts are based on hearsay, repeating affirmations from sources who have no idea about how the Planck units have been defined in 1899 and about how systems of fundamental units of measurement are defined and what they mean. Apparently the only reason why the Planck units have been picked for this purpose is that in this system the unit of length happens to be much smaller than an atom or than its nucleus, so people imagine that if the current model of space breaks at some scale, that scale might be this small.