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It's not a big deal to be implemented and NIST has results that can be used for comparison.

Get the values closer to the NIST values.
There are various places where this can be improved, for example the distance from where the integration starts can be adjusted (it's different depending on the level but far from perfect), maybe also do a match for derivatives in the meeting point when shooting from both zero and 'infinity'...

Probably it won't happen, but it's a possible enhancement.

See 'How to build an Atom' and https://arxiv.org/abs/1209.1752
The later describes also how to use a non-uniform grid. It's not a big deal to derive that one, though.

The class for Runge-Kutta solvers can be taken from the ElectricField or the CompLotkaVolterra project.

This is another possible enhancement.

Probably this will not happen soon, but it's reasonably simple to implement.

There are some exceptions to the Aufbau principle, for example for gold, thorium or uranium.