Is our physics and system of units based on time (second) or the speed of light?

The speed of light in vacuum is stated in our physics as a universal physical constant, c, when measured locally, in vacuum.

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most commonly associated with light, it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum (including electromagnetic radiation and gravitational waves). Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.

https://en.wikipedia.org/wiki/Speed_of_light

It basically defines the speed of causality.

The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the charge of the electron, which can be observed and measured with great accuracy.

So it says here that the base units are derived from the speed of light and the charge of the electron.

Now we are using SI units, and it defines the second as the base unit. Everything else is derived.

The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. Within the context of the SI, the second is the coherent base unit of time, and is used in the definitions of derived units.

So basically the SI itself has a contradiction in the definition of its base unit.

https://en.wikipedia.org/wiki/International_System_of_Units

It is not clear if the universal constant like the speed of light is the base unit, or it is the second (based on the caesium atom). Which one is derived from which, and is the speed of light the universal constant or is it the second?

I might be saying, that the transition time between the hyperfine levels of the caesium atom are constrained by the speed of causality (speed of light), so this becomes circular.

Question:

1. Is our physics and our SI based on the universal constant of speed of light or time (second), and which one is the derived unit?