While I know nothing about ESP-01 other than I have been asked for a part before, this web site
after translating the pins from a Uno to a nano indicates this should work.
the breadboard isn’t really needed, if you can connect the 3.3V nano pin to 2 pins on the ESP-01.
the sketch the above screen shot came from
ESP8266 ESP01.fzpz (17.5 KB)
Peter