Is it correct to say that the pKa is the pH at equilibrium?
$\mathrm{p}K_\mathrm{a}$ and $\mathrm{pH}$ are apples and oranges.* We can't equate them on a graph. The correct wording should rather be that the $\mathrm{pH}$ at which the concentration ratio of an acid and its conjugate base is equal to $1,$ then the $\mathrm{pH}$ is numerically equal to $\mathrm{p}K_\mathrm{a}.$

* It will be another painful story if one begins to argue on the units of $\mathrm{pH}$ and $\mathrm{p}K_\mathrm{a}.$ They are dimensionless. Just a subtle point $\mathrm{p}K_\mathrm{a}$ is constant as long as the temperature/pressure is constant. It is not always a constant.