I read the first 25 pages to see if someone had a problem solved like mine. Zero.
My ESP-01 acts like it isn't there. It is powered with a buck adjustable set to 3.31V with RST pin going direct to +3.3V, CH_EN pin going direct to 3.3V as well. It has a red LED that is lit that I assume is power and a blue LED that lights briefly for power-on.
WiFiEsp is the most comprehensive library, it handles the AT commands of course, ... it returns
[WiFiEsp] Initializing ESP module
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] Cannot initialize ESP module
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
********************************************** Firmware version > FAILED (actual="", expected="1.5.2")
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
********************************************** Status is (WL_DISCONNECTED) > FAILED (actual=255, expected=3)
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] Failed connecting to JMR
********************************************** Connect > FAILED (actual=2, expected=1)
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
********************************************** Check status (WL_CONNECTED) > FAILED (actual=255, expected=1)
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
********************************************** Check SSID > FAILED (actual="", expected="JMR")
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
********************************************** Check IP Address > FAILED (actual=0, expected=0)
IP Address: 0.0.0.0
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
MAC: 0:0:0:0:0:0
[WiFiEsp] >>> TIMEOUT >>>
********************************************** Disconnect > PASSED
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
********************************************** Check status (WL_DISCONNECTED) > FAILED (actual=255, expected=3)
[WiFiEsp] >>> TIMEOUT >>>
[WiFiEsp] No tag found
********************************************** IP Address > PASSED