CC2642R: how to use uart interrupt,

The example is not for me, I want use rx interrupt,. 'UART2_Mode_CALLBACK' mode ： When is the read callback function called? What does it do? Why did I turn on the callback mode and keep reading the loop. I can read it. Isn't it gilding the lily if I turn on the callback

The uart2callback example certainly uses RX interrupts and a callback:

    /* Create a UART in CALLBACK read mode */
    UART2_Params_init(&uartParams);
    uartParams.readMode     = UART2_Mode_CALLBACK;
    uartParams.readCallback = callbackFxn;

A description is provided in the UART2 TI Driver API:

"UART2_Mode_CALLBACK is nonblocking and UART2_read() and UART2_write() will return while data is being sent in the context of a hardware interrupt. When all data has been read from, or written to the hardware FIFO, the UART2 driver will call the user's callback function, and the driver is ready to accept another read or write operation."

"In UART2_Mode_CALLBACK, UART2_read() does not block task execution. Instead, a callback function specified by UART2_Params::readCallback is called when the transfer is finished (UART2_ReadReturnMode_FULL), or reception has become inactive (UART2_ReadReturnMode_PARTIAL). The callback function can occur in the caller's context or in HWI context, depending on the device-specific implementation. An unfinished asynchronous read operation must always be cancelled using UART2_readCancel() before calling UART2_close()."

I did not understand you last sentences.  Perhaps you should provide code excerpts alongside clearly written descriptions of the issue you are encountering.

Regards,
Ryan