Violation of conservation of angular momentum

You cannot consistently consider a charged particle without considering its electromagnetic field as well. A system of charged particles plus their field is “closed” and its energy, momentum, and angular momentum are conserved. Without the field it is not closed and these quantities are not conserved.

A single non-interacting charged particle does not transfer energy, momentum, or angular momentum to the field. This is calculable from the equations for its field. In its rest frame, the field is just an electrostatic Coulomb field. Only fields with both electric and magnetic components transfer energy, momentum, and angular momentum from place to place.

Interacting particles accelerate, causing the field to have a magnetic part, as seen in the Lienard-Wiechert potentials. Then the Poynting vector is nonzero and energy (and also momentum and angular momentum) flows through the electromagnetic field.

The case of two charges that magnetically interact can be discussed in a much simpler manner. We are all familiar with the concept of potential energy and know that kinetic energy is not separately conserved : only the sum of kinetic and potential energy is. In special relativity energy is the time component of four momentum. For the same reason kinetic energy is linked to kinetic momentum , potential energy is connected to potential momentum. The electromagnetic vector potential should thus be seen as producing potential momentum. While kinetic momentum, $m\bf v$, is not conserved, the sum of kinetic and potential momentum, $m{\bf v} + q\bf A$, is conserved in the case of two magnetically interacting charges.