Arduino Nano disconnecting from PC on plugging in 3.3v NRF24L01 into PCB
In your design the 3.3V power to NRF24L01 is coming from Arduino Nano USB interface chip, which is FT232RL. The internal FT232 regulator can only supply 50 mA, "Up to 50mA can be drawn from this pin to power external logic if required". the FT232 specs says.

The 50 mA regulator is a pretty weak source. While the spec says the NRF24L01 draws only "11 mA" in transmit", I suspect it draws much more than that in bursts. More, the NRF24L01 requires the power to be bypassed by "high performance RF capacitor" of 4.7 uF. Your board has a junky aluminum electrolytic cap, which likely has no bypass capability at burst frequencies the NRF24L01 operates at.

So essentially you inject huge noise into USB PHY power rail, and the USB signals (or their frequency) are likely got severely distorted, which causes the host to detect massive errors and shut the port down.

To fix the problem you need to place a 10 uF low-ESR ceramic capacitor right between pins of NRF24L01 2x4 header, and better de-couple it from Arduino pin14 (3.3V) with a good ferrite bead or good inductor, to filter the noise from entering the FT232 IC.