Blinking LED along with NRF24L01

This is your function loop like posted in post #1

What your code is doing is executing your function doBlink();
when ever your Arduino pro micro is "awake" = not sleeping

What your function doBlink is doing is
once every second switch IO-pin 1 HIGH for 10 milliseconds
then switch low again.

though IO-pin 1 is used for serial transmitting at the same time
what might works is using a operational amplifier chip like an MCP6042
https://www.mouser.de/ProductDetail/Microchip-Technology/MCP6042-E-P?qs=MvcPkWSywowxarV%2FCKQAcQ%3D%3D
wired as a voltage-follower.

An LED draws a current 5 mA to 20 mA. Which will have an impact on the serial inetrface.
the input-resistance of an OpAmp-voltage-follower is minimum 10 MOhm high which means the current is supertiny 5V / 10000000 Ohm = 0.5 microampere = 0.0000005 A
which has no practical effect on the serial connection.
The led is then connected between to the output of the OpAmp and a 330 Ohm-resistor towards ground

best regards Stefan