Question about Fujifilm BC-W235

No. A "normal" USB-C charging cable for mobile phones with the corresponding charger is sufficient.

This charger can be used to charge two batteries (NP-W235) in parallel. A mains adapter (AC-5VJ) and a USB cable (type C) are required to charge the batteries with BC-W235.
The charging cable and mains adapter were supplied with the charger when it was purchased. No additional mains adapter is required.