Center-Aligned PWM when to trigger current measurement STM32F4
Yes, STM32F410 cannot measure multiple voltages at once. It only has one ADC and the channels are merely multiplexed. If you are set on an STM32 you need one with an ADC for each simultaneous measurement (typically up to 3, more on STM32F3).

As talked about in the comments: another issue was sampling time. OP set the sampling time to 480 cycles at a 25 MHz clock which is 19,2us - that's too long for this application.