When the 410c was designed it was decided to NOT support charging with the charging circuitry built into the PMIC.
There are litteraly hundreds of things that you have to set up correctly to safely charge a battery. The settings are very specific to each battery module, and depend on the chemistry and the supplier recommendations as well as the capacity of the battery and the physical mounting of the battery. Far too many variables. Most of the parameters are set in the proprietary binaries long before lk starts and most customers do not have access to the proprietary binaries.
I don’t think you will ever get the battery charger in the PMIC running and even if you do, your system will be a fire hazzard without the correct settings.
If you really need battery charging on your system, use an external third party chip that you can program correctly for your battery.