I checked out some resources on how the constant of proportionality of the Coulomb force was discovered and to my surprise, I found out that it was mathematically derived (unlike the Cavendish experiment for the gravitational constant) by using Gauss's law.
When I searched for the proof of Gauss's law, it used Coulomb's law WITH THE COULOMB CONSTANT AS $1/4πε$. Surely I am missing something, can you guide me?
Links - For Coulomb's constant, check out the 'Value of the constant' section https://en.wikipedia.org/wiki/Coulomb%27s_constant
For proof of Gauss's law, check out 'Deriving Gauss' law from Coulomb's law' in 'Relation to Coulomb law' section https://en.wikipedia.org/wiki/Gauss%27_law