When HAL doesn't work, dont use it.
Neither RCC nor UART is too complicated on the STM32F0 series. Writing a driver should take a lot less time than finding out what HAL doesn't do right, and wait for the next release of HAL for it to be fixed.
Try this as a replacement for SystemClock_Config() if you suspect that HAL did not get your clock setup right.
FLASH->ACR |= FLASH_ACR_LATENCY; // ensure flash works with the higher clock
FLASH->ACR |= FLASH_ACR_PRFTBE;
RCC->CR |= RCC_CR_HSION; // start HSI
while((RCC->CR & RCC_CR_HSIRDY) == 0) // wait for HSI startup
;
RCC->CFGR &= ~RCC_CFGR_SW; // switch system clock to HSI
while((RCC->CFGR & RCC_CFGR_SWS) != 0) // wait for the switchover to complete
;
RCC->CR &= ~(RCC_CR_PLLON | RCC_CR_CSSON | RCC_CR_HSEON); // stop PLL,CSS,HSE
while((RCC->CR & RCC_CR_PLLRDY) != 0) // wait for PLL to stop
;
RCC->CFGR = 0b0100U << RCC_CFGR_PLLMUL_Pos; // 0100: PLL input clock x 6
RCC->CR |= RCC_CR_PLLON; // turn PLL on
while((RCC->CR & RCC_CR_PLLRDY) == 0) // wait for PLL startup
;
RCC->CFGR |= RCC_CFGR_SW_PLL; // switch system clock to PLL
while((RCC->CFGR & RCC_CFGR_SWS) != RCC_CFGR_SWS_PLL) // wait for the switchover to complete
;
Half of it might be superfluous, I know. If the frequency still does not look right, adjust RCC->CFGR = 0b0100U << RCC_CFGR_PLLMUL_Pos; if necessary.
Then proceed to set up the UARTs as described in the reference manual. For simple RX/TX, this would do
USARTx->CR1 = 0;
USARTx->BRR = 48000000/baudrate;
USARTx->CR1 = USART_CR1_TE | USART_CR1_RXNE | USART_CR1_UE;
