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On the current limiting problem ...
You'd better step down the voltage with a resistor, which is 3V. 150 ohm is required when the minimum current is 200mA, and 75 ohm is required when the maximum current is 400mA. It is recommended to use a resistor of 100- 150 ohm (smaller charging current is beneficial to battery life).

Using resistance to reduce voltage actually has automatic protection function. When the charging current is too large, the voltage drop across the resistor will further increase, reducing the output voltage and the increasing trend of the output current.

When you use the output of the voltage regulator, it is actually a constant voltage source. It is actually harmful to keep the output of 5V when the current is high.