Problem with using power bank for modem with dc dc booster
Nothing says that your boost converter module can supply the current your device needs. You'll need to find the datasheet of your module (not just the chip on it), and verify, together with the datasheet of your modem, that it can indeed provide the current.
But also, and very alarmingly: Twisting wire around solderpads is a totally insufficient method to connect things electrically. At least one of your connections has a high resistance, and that leads to a voltage drop as soon as any current is draw.
Solder your wires to the board.  What you have will not work reliable, even if your module can indeed theoretically supply enough current.