Different buffer size for different serial port of Mega2560 ?

The TX buffer in the Serial library is to allow that the sketch continues, and meanwhile the data will be transmitted from the buffer with interrupts.

The TJC3224T022_011N is the chinese version of a Nextion display. It has been made specifically for China. If you are from the U.S.A. or Europe, you should get a Nextion version. They have different firmware to avoid that others use the Chinese version.

The default baudrate of the Nextion displays is 9600 baud. I have my Nextion running at 38400 baud.
For uploading new firmware, it does support 115200 baud. I don't know if normal texts allow that high baudrate.

Do you use the Nextion Arduino library ? I am not very happen with that library. That library has many delays and waits for a reply and is slow and could miss data. Using 115200 will not make that library faster. It might make the problems with that library even worse.

I have turned off the reply with "bkcmd=0" and use my own functions to transmit data to the display.

Can you do more tests ?
For example with other baudrates, with the reply turned off and with your own functions.

  nexSerial.print( "text1.txt=\"Hell World\"");   // text1 is the name of the Nextion item
  nexSerial.print( "\xFF\xFF\xFF");

Be careful when changing the baudrate. I have lost my Nextion display a couple of times, because the baudrate was set to an unknown value. I had to write a special sketch that tries evertything with 3% increase of the baudrate.