If a power bank accepts multi voltage input, will the lowest accepted voltage choice cause bad effects on the battery?
Summary:  It is likely that -

Using a 12V supply will very substantially undercharge your internal battery.
This will lower the capacity per charge but increase the lifetime capacity and cycle life of the battery.

Use of a 14.8V or higher supply as recommended by the manufacturer will allow full capacity charging.



It is likely that the following applies. This is 'professional guestimate' but has a good chance of being correct or correct-enough.

The powerbank uses 3S LiIon batteries

The internal converter when charging the batteries is a buck converter

There is a maximum upper input current limit.


The specified 14.8 V recommended minimum Vin can be explained by the fact that each internal cell requires 4.2V to charge fully.
A competent charger would allow lowering OR raising of Vin to suit the battery (buck-boost) but the easier / cheaper solution is reduction only (buck).
If the charger can not boost voltage then Vin must be &gt;= 3 x 4.2V + a headroom allowance.
3 x 4.2 = 12.8V.
They have allowed themselves 2V &quot;headroom&quot;.
The statement that a higher Vin allows a greater charge rate can be explained by their being some max Iin specification. Power in max = Vin x Iin_max. More Vin = more power.
The boost converter will transform this to 19 20 24V as required.
A linear regulator or buck converter will step it down when Vbattery is &gt; Vout.