STM32F437 UART doesn't work at 3.6V~4.2V(lithium battery)
The operating voltage range is 1.8 to 3.6 Volts. It means that if the supply voltage is any higher than 3.6 Volts, the device might malfunction.

There is an absolute maximum rating of 4.0 Volts. It means that the device will survive a supply voltage up to 4.0 Volts without permanent damage, and will be able to function again after a reset. Above 4.0 Volts you can expect permanent damage.

There are 5V tolerant I/O pins on the device, so it can work with I/O signals up to 5V, but the power must still be in the 1.8V-3.6V range.

You can check the exact power requirements in the Electrical characteristics chapter of the datasheet.

Also note that all VDD pins should be connected to the power source, not just one of them. Check the decoupling capacitor requirements too.