UART Receive issue

On Custom board is clock source (HSE) different? Have you changed HSE_VALUE define to reflect this? Baud rate computation depends on this being correct.

I use my PC through a UART to USB chip.

/* USER CODE BEGIN Header */
/**
 ******************************************************************************
 * @file : main.c
 * @brief : Main program body
 ******************************************************************************
 * @attention
 *
 * Copyright (c) 2023 STMicroelectronics.
 * All rights reserved.
 *
 * This software is licensed under terms that can be found in the LICENSE file
 * in the root directory of this software component.
 * If no LICENSE file comes with this software, it is provided AS-IS.
 *
 ******************************************************************************
 */
/* USER CODE END Header */
/* Includes ------------------------------------------------------------------*/
#include "main.h"

/* Private includes ----------------------------------------------------------*/
/* USER CODE BEGIN Includes */
#include <string.h>

/* USER CODE END Includes */

/* Private typedef -----------------------------------------------------------*/
/* USER CODE BEGIN PTD */

/* USER CODE END PTD */

/* Private define ------------------------------------------------------------*/
/* USER CODE BEGIN PD */

/* USER CODE END PD */

/* Private macro -------------------------------------------------------------*/
/* USER CODE BEGIN PM */

/* USER CODE END PM */

/* Private variables ---------------------------------------------------------*/
UART_HandleTypeDef hlpuart1;

/* USER CODE BEGIN PV */

char rcv_msg[20];
unsigned char msg_ptr;
uint8_t rcv_char;
const char delimiter = '\n';
unsigned char msg_available = 0;

/* USER CODE END PV */

/* Private function prototypes -----------------------------------------------*/
void SystemClock_Config(void);
static void MX_GPIO_Init(void);
static void MX_LPUART1_UART_Init(void);
/* USER CODE BEGIN PFP */

/* USER CODE END PFP */

/* Private user code ---------------------------------------------------------*/
/* USER CODE BEGIN 0 */

void HAL_UART_RxCpltCallback(UART_HandleTypeDef *huart)
{
	msg_available = 1;
	if(rcv_char == '\n')
	{
		msg_available = 1;
		msg_ptr = 0;
	}
	else
	{
		rcv_msg[msg_ptr] = rcv_char;
		msg_ptr++;
	}
	HAL_UART_Receive_IT(&hlpuart1, (uint8_t*)&rcv_char, 1);
}


/* USER CODE END 0 */

/**
 * @brief The application entry point.
 * @retval int
 */
int main(void)
{
 /* USER CODE BEGIN 1 */

 /* USER CODE END 1 */

 /* MCU Configuration--------------------------------------------------------*/

 /* Reset of all peripherals, Initializes the Flash interface and the Systick. */
 HAL_Init();

 /* USER CODE BEGIN Init */

 /* USER CODE END Init */

 /* Configure the system clock */
 SystemClock_Config();

 /* USER CODE BEGIN SysInit */

 /* USER CODE END SysInit */

 /* Initialize all configured peripherals */
 MX_GPIO_Init();
 MX_LPUART1_UART_Init();
 /* USER CODE BEGIN 2 */


 //printf("Hello World %d\r\n", test);
 HAL_UART_Transmit(&hlpuart1, (uint8_t*)"Hello World\r\n", 13, 1000u);

 HAL_UART_Receive_IT(&hlpuart1, (uint8_t*)&rcv_char, 1);

 /* USER CODE END 2 */

 /* Infinite loop */
 /* USER CODE BEGIN WHILE */
 while (1)
 {
 /* USER CODE END WHILE */

 /* USER CODE BEGIN 3 */
 	if(msg_available)
 	{
 		msg_available = 0;
 		HAL_UART_Transmit(&hlpuart1, (uint8_t*)"msg_available\r\n", 15, 1000u);
 		if(strstr(rcv_msg ,"MOTOR"))
 		{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"MOTOR test has been selected\r\n", 31, 1000u);
 		}
 		else if(strstr(rcv_msg ,"TEMP"))
 		{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"TEMP test has been selected\r\n", 31, 1000u);
 		}
 		else if(strstr(rcv_msg ,"SONAR"))
 			{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"SONAR test has been selected\r\n", 31, 1000u);
 			}
 		else if(strstr(rcv_msg ,"CONTACT_SENS"))
 			{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"CONTACT_SENS test has been selected\r\n", 37, 1000u);
 			}
 		else if(strstr(rcv_msg ,"WEIGHT"))
 			{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"WEIGHT test has been selected\r\n", 31, 1000u);
 			}
 		else if(strstr(rcv_msg ,"ENCODER"))
 			{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"ENCODER test has been selected\r\n", 32, 1000u);
 			}
 		else if(strstr(rcv_msg ,"STEPPER"))
 			{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"STEPPER test has been selected\r\n", 32, 1000u);
 			}
 		else if(strstr(rcv_msg ,"T_HUM"))
 			{
 			HAL_UART_Transmit(&hlpuart1, (uint8_t*)"TEMP_HUM test has been selected\r\n", 33, 1000u);
 			}
 		rcv_msg[0] = '\0';
 	}
 }
 /* USER CODE END 3 */
}

/**
 * @brief System Clock Configuration
 * @retval None
 */
void SystemClock_Config(void)
{
 RCC_OscInitTypeDef RCC_OscInitStruct = {0};
 RCC_ClkInitTypeDef RCC_ClkInitStruct = {0};

 /** Configure the main internal regulator output voltage
 */
 HAL_PWREx_ControlVoltageScaling(PWR_REGULATOR_VOLTAGE_SCALE1);

 /** Initializes the RCC Oscillators according to the specified parameters
 * in the RCC_OscInitTypeDef structure.
 */
 RCC_OscInitStruct.OscillatorType = RCC_OSCILLATORTYPE_HSI;
 RCC_OscInitStruct.HSIState = RCC_HSI_ON;
 RCC_OscInitStruct.HSICalibrationValue = RCC_HSICALIBRATION_DEFAULT;
 RCC_OscInitStruct.PLL.PLLState = RCC_PLL_NONE;
 if (HAL_RCC_OscConfig(&RCC_OscInitStruct) != HAL_OK)
 {
 Error_Handler();
 }

 /** Initializes the CPU, AHB and APB buses clocks
 */
 RCC_ClkInitStruct.ClockType = RCC_CLOCKTYPE_HCLK|RCC_CLOCKTYPE_SYSCLK
 |RCC_CLOCKTYPE_PCLK1|RCC_CLOCKTYPE_PCLK2;
 RCC_ClkInitStruct.SYSCLKSource = RCC_SYSCLKSOURCE_HSI;
 RCC_ClkInitStruct.AHBCLKDivider = RCC_SYSCLK_DIV1;
 RCC_ClkInitStruct.APB1CLKDivider = RCC_HCLK_DIV1;
 RCC_ClkInitStruct.APB2CLKDivider = RCC_HCLK_DIV1;

 if (HAL_RCC_ClockConfig(&RCC_ClkInitStruct, FLASH_LATENCY_0) != HAL_OK)
 {
 Error_Handler();
 }
}

/**
 * @brief LPUART1 Initialization Function
 * @PAram None
 * @retval None
 */
static void MX_LPUART1_UART_Init(void)
{

 /* USER CODE BEGIN LPUART1_Init 0 */

 /* USER CODE END LPUART1_Init 0 */

 /* USER CODE BEGIN LPUART1_Init 1 */

 /* USER CODE END LPUART1_Init 1 */
 hlpuart1.Instance = LPUART1;
 hlpuart1.Init.BaudRate = 115200;
 hlpuart1.Init.WordLength = UART_WORDLENGTH_8B;
 hlpuart1.Init.StopBits = UART_STOPBITS_1;
 hlpuart1.Init.Parity = UART_PARITY_NONE;
 hlpuart1.Init.Mode = UART_MODE_TX_RX;
 hlpuart1.Init.HwFlowCtl = UART_HWCONTROL_NONE;
 hlpuart1.Init.OneBitSampling = UART_ONE_BIT_SAMPLE_DISABLE;
 hlpuart1.Init.ClockPrescaler = UART_PRESCALER_DIV1;
 hlpuart1.AdvancedInit.AdvFeatureInit = UART_ADVFEATURE_NO_INIT;
 if (HAL_UART_Init(&hlpuart1) != HAL_OK)
 {
 Error_Handler();
 }
 if (HAL_UARTEx_SetTxFifoThreshold(&hlpuart1, UART_TXFIFO_THRESHOLD_1_8) != HAL_OK)
 {
 Error_Handler();
 }
 if (HAL_UARTEx_SetRxFifoThreshold(&hlpuart1, UART_RXFIFO_THRESHOLD_1_8) != HAL_OK)
 {
 Error_Handler();
 }
 if (HAL_UARTEx_DisableFifoMode(&hlpuart1) != HAL_OK)
 {
 Error_Handler();
 }
 /* USER CODE BEGIN LPUART1_Init 2 */

 /* USER CODE END LPUART1_Init 2 */

}

/**
 * @brief GPIO Initialization Function
 * @PAram None
 * @retval None
 */
static void MX_GPIO_Init(void)
{
/* USER CODE BEGIN MX_GPIO_Init_1 */
/* USER CODE END MX_GPIO_Init_1 */

 /* GPIO Ports Clock Enable */
 __HAL_RCC_GPIOA_CLK_ENABLE();

/* USER CODE BEGIN MX_GPIO_Init_2 */
/* USER CODE END MX_GPIO_Init_2 */
}

/* USER CODE BEGIN 4 */

/* USER CODE END 4 */

/**
 * @brief This function is executed in case of error occurrence.
 * @retval None
 */
void Error_Handler(void)
{
 /* USER CODE BEGIN Error_Handler_Debug */
 /* User can add his own implementation to report the HAL error return state */
 __disable_irq();
 while (1)
 {
 }
 /* USER CODE END Error_Handler_Debug */
}

#ifdef USE_FULL_ASSERT
/**
 * @brief Reports the name of the source file and the source line number
 * where the assert_param error has occurred.
 * @PAram file: pointer to the source file name
 * @PAram line: assert_param error line source number
 * @retval None
 */
void assert_failed(uint8_t *file, uint32_t line)
{
 /* USER CODE BEGIN 6 */
 /* User can add his own implementation to report the file name and line number,
 ex: printf("Wrong parameters value: file %s on line %d\r\n", file, line) */
 /* USER CODE END 6 */
}
#endif /* USE_FULL_ASSERT */

Here's my complete main.c code 

How do I check parity / framing ?

Here's the Reference Manual, explains the bit flags. The 8 (bit 3) is the Overrun Error

https://www.st.com/resource/en/reference_manual/rm0440-stm32g4-series-advanced-armbased-32bit-mcus-stmicroelectronics.pdf

> There may be noise, e.g. if you connect connectors, or there may be bad ground connection... Oscilloscope is your friend.

Here's a picture of the signal received on RX pin.

Signal seems OK.

> If you observe the UART Rx data register in debugger, the RXNE flag gets cleared...

I don't get into the interrupt handler with only one char and without debugger 

I've setup an interrupt on a GPIO and it doesn't fire also. 

EXTI ?

Start by establishing the EXTIxx_IRQHandler() that's called by the NVIC, you are then responsible for calling into the HAL which then calls your function.