HAL_SPI_Transmit() Size, is it defined as a byte or a word?

Look at the library source code, it is provided.

Pretty sure it is a unit count. If you configured the SPI in 16-bit mode it will be words, and bytes in 8-bit mode.

Disclaimer: Not an expert.

tl;dr : 16-bit words 

Looking at the source code in stm32f4xx_hal_spi.c, the argument in question (1 or 2) is received as parameter uint16_t Size.

HAL_StatusTypeDef HAL_SPI_Transmit(SPI_HandleTypeDef *hspi, uint8_t *pData, uint16_t Size, uint32_t Timeout)

uint16_t Size is assigned to both hspi->TxXferSize and hspi->TxXferCount.

 /* Set the transaction information */
 hspi->State = HAL_SPI_STATE_BUSY_TX;
 hspi->ErrorCode = HAL_SPI_ERROR_NONE;
 hspi->pTxBuffPtr = (uint8_t *)pData;
 hspi->TxXferSize = Size;
 hspi->TxXferCount = Size;

The routine loops through hspi->TxXferCount and decrements down to zero. I believe the answer to your question is found herein. DR is loaded with a 16-bit word along with decrement of TxXferCount; the load and decrement are 1-to-1. If Size was 8-bit char, we might assume it would be 2-to-1. This suggests the argument Size is 16-bit words.

/* Transmit data in 16 Bit mode */
 while (hspi->TxXferCount > 0U)
 {
 /* Wait until TXE flag is set to send data */
 if(__HAL_SPI_GET_FLAG(hspi, SPI_FLAG_TXE))
 {
 hspi->Instance->DR = *((uint16_t *)pData);
 pData += sizeof(uint16_t);
 hspi->TxXferCount--;
 }
 else
 {
 /* Timeout management */
 if((Timeout == 0U) || ((Timeout != HAL_MAX_DELAY) && ((HAL_GetTick()-tickstart) >= Timeout)))
 {
 errorcode = HAL_TIMEOUT;
 goto error;
 }
 }
 }