Symmetric, rational and infinitely many $(23_4)$ configurations, and the end of the existence problem for geometric $(n_4)$ configurations

A geometric $(n_4)$ configuration is a set of $n$ points and $n$ lines in the real projective plane such that every point lies on exactly four of the lines and every line contains exactly four of the points. The question of which $n$ admit such a configuration was posed by Grünbaum in 2000, and succ