How should one visualize the *electric field* formed from a point charge moving at constant velocity?

So we all know how the magnetic field looks like ( qv x r )
While trying to visualize the electric field I got a little bit confused.

Because we are not in electrostatic anymore I don’t know if I can imagine the electric field lines coming out (or into) a charge and staying constant on it while it travel in a constant speed.
I assume that this charge is exerting force on other charged particles (which are in rest) and we can calculate it any time just by knowing the charges and the distance between them.
If that’s correct I think that there is no reason for the electric field lines of a charged particle held constant and travel with the charge.

If that’s not the case , so what is happening to the electric field produced by a resting charge when it start moving and finally gets to a constant speed ?

Thank u all