The first part of the message (“Refinement limit exceeded for auto-refinement. The mesh is valid but may not be adequately refined”) is a warning and is probably indicating to the source of the problem. The warning tells us that the mesh is not refined enough. The solution to this problem is discussed in this KX post.
The transient solver performs a steady state simulation for the conditions at t=0 and uses that as the initial solution for the transient simulation. The error message “Initialization failed to converge charge update” means that the steady state solution failed. This could be due to the non-refined mesh. Also, if the initial condition at t=0 (such a voltages at contacts) is far from equilibrium (large voltages) then the solver may fail to find the steady state solution as well. In such a case, you can first perform a steady state simulation and gradually sweep the voltage up to the desired level and then use that solution to initialize your transient simulation. This is described in this other KX post.