Are RX0/TX0 somehow connected to the USB virtual UART in the Nano?
Whenever I have connected something (another hardware-USB-UART adapter), it gives an interference with the AVRDUDE programmer in the Arduino IDE (Timeout) when uploading:
avrdude: Version 6.3-20190619
Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
Copyright (c) 2007-2014 Joerg Wunsch
System wide configuration file is "/Users/kuku/Library/Arduino15/packages/arduino/tools/avrdude/6.3.0-arduino17/etc/avrdude.conf"
User configuration file is "/Users/kuku/.avrduderc"
User configuration file does not exist or is not a regular file, skipping
Using Port : /dev/cu.usbserial-1420
Using Programmer : arduino
Overriding Baud Rate : 115200
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 2 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 3 of 10: not in sync: resp=0x00
...
avrdude done. Thank you.
Problem uploading to board. See https://support.arduino.cc/hc/en-us/sections/360003198300 for suggestions.