HAL_UART_Transmit is blocking, which means it will not return until the transmission is done. There is no need to wait between calls.
HAL_UART_Transmit_IT and HAL_UART_Transmit_DMA happen asynchronously. You will need to wait for the transmission to complete and the state to return to ready before calling them again. Calling them too soon will result in them returning HAL_BUSY.
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