Linear Regulator Dropouts
The linear voltage regulators found on that board are going to expect more than 5V at the barrel jack, because they require a minimum "drop out" voltage. The AMS1117 that is on that board, so far as I can tell, has a drop out voltage up to 1.3V. So you would want at least 6.3V (perhaps better 7V) at the barrel jack in order to get 5V out of it.
So the NodeMCU board may be seeing 5 - 1.3 or 3.7V at the input to its 3.3V regulator, which also requires its own drop out. The output of that 3.3V regulator may then be significantly below what the esp8266 specified operating voltage range.
So I did the tests mentioned in the comments, just to illustrate the problem. And the results are about as expected.
I altered the stock blink sketch that comes with IDE version 1.8.13 to use LED_BUILTIN (as opposed to 9) in the pinMode and digitalWrite calls.
I changed the LOW period, which is LED ON for my board, to 10000ms so that my voltmeter would have time to settle on a voltage test across the LED.
And I uploaded to the board, a NodeMCU 1.0 clone by Hitletgo.
When powered on its USB micro b jack, 3.3V labeled pin of the broad measuring 3.30 V. The LED color is blue, it is bright and it is dropping 2.66V.
Then I switched to powering the NodeMCU board by via of VIN pins from the YwRobot regulator board. I provided 5.05V to the barrel jack. To not great surprise, it does not blink.
The voltage out of regulator board was 3.26V. To be clear, I have this jumper for 5V. As a sanity check, I jumpered it for 3.3V and got about 2.5V out of it. Again, this is unsurprising because it also needs a dropout voltage.
I then measured the "3.3V" header line on the NodeMCU itself to be 2.14 V. Without sufficient voltage into the 3.3V regulator, it is not providing 3.3V out. And what it is producing is below that LED forward voltage when lit. So it is not surprising that it is not lit.
The ESP8266 technical specifications suggest that it can run down to 1.8V. So just for the hell of it I connected the board back to USB and updated the blink sketch to "blink" D8 (or GPIO15) 4 seconds on, 4 seconds off. I did not attach anything to this pin except the voltmeter.
I then reconnected the board to the test rig and found with a meter that it is "blinking" D8 just fine with a logic level consistent with the voltage the ESP8266 is actually receiving.
So in summary, the arrangement here is running the ESP8266 but there is not enough available voltage for it to light the LED. And it is very likely the exact same thing is happening for you.