Read the section 8.3.10 of the datasheet (https://www.ti.com/lit/ds/symlink/ads1232.pdf?ts=1639310753629&ref_url=https%253A%252F%252Fwww.google.com%252F)
You should configure the USART peripheral to synchronous receiver (look at the waveforms in the datasheet for phase and polarity configuration).
I guess you can wait for the USART RX pin to go low (polling/interrupt), then and start receiving the desired bytes (with HAL if it works for you). Then stop reception and wait for the next falling edge.
You can let CUBE configure your USART Peripheral. If you want to poll it should work, if I remember correctly. Try, eventually.
If you want to get an interrupt it's a little bit more tricky. I'd go like this: CUBE initializes the peripheral, then you have to do manually configure the GPIO pin to Exti and change it's mode to Exti. Then, when you get interrupt, you reinitialize the pin as uart RX and start receiving. When finished receiving the data, you reconfigure the pin to Exti.
