Electrical – Charging a protected 18650 cell

Your idea of grounding the step-down regulator to the cell it is charging is quite clever, but it won't work properly because its supply current also flows through all the cells below it. This will cause the lower 3 cells to get varying amounts of uncontrolled charge current that their associated chargers cannot get rid of, which will eventually cause them to become unbalanced and possibly overcharged (which is potentially very dangerous).

To do it properly you need 4 fully isolated power supplies, or use a single 4 cell charger and wire a balancer onto the battery. Cheap 4 cell balancer boards are readily available on eBay and elsewhere. These often also have over-charge and over-discharge protection.

If you use a protection board then the charger can just be a regulator with adjustable current and voltage, like this.

A charger built with these components may be more efficient, more reliable, and possibly even cheaper than a bunch of step-down regulators and TP4056 chargers.

That BMS looks identical to one that I've used and it does NOT do balancing or proper charging. Just protecting from over current, over voltage and under voltage - all of which are very important.

You will need to add balance wires and get a balance charger for this battery.

Balance wires are easy - they go exactly where the bms wires go - one to each pos and neg of each cell. The balance charger will have a slot for those wires.

I recommend looking at the IMAX b6 charger because it is the cheapest balance charger I have seen and seems to work reasonably well up to batteries with 6s or less.