Given the information you provided I see at least 2 possibilities:
The common (aka ground) from the 5V switcher is wired such that current from the LEDs to the common of the switching regulator is upsetting the "ground" power of the NRF and Nano.
More likely, switching noise from the 5v switcher is causing excessive RF noise and interfering with the NRF.
Suggestion for 1)
Check to see where the common of 5V switcher is connected to the circuit. It should be as close to the battery common as possible.
Note: This may sound a little condescending but there is no such thing as ground. I've found the word "ground" gives folks the impression of some absolute condition. It is not. I believe the term "return" best describes the function of what most call ground. Also used is common.
Also note, wires are really low value resistors. And fast switching times can result in current far above what most folks think. These two together can result in the instantaneous voltage on one physical end of a circuit to be vastly different from the other end. So look at your physical layout.
An common (physical) wiring scheme that often works well is the "star" connection. In your circuit the common of the NRF, Nano and LEDs would come together at the battery negative terminal.
Suggestion for 2)
Add a 10µF and a 0.01µf in parallel as close to the 5V switcher input as possible. Repeat the same for the output.
BTW of the two capacitors, the 0.1µf is the most important. The 10µf might be overkill (didn't know you component details) it could be 1µf or even left out. Give it a try if you want.
I tried only 0.1uF, latency dropped to 200. Then I added 10uF and it dropped to 60ms again.
10uF and 0.1uF seems to be the best combination for NRF24l01.
You might try a similar pair on the output of the 5V switcher. Even if it doesn't change the latency it might be a good idea. Sometimes noise and pop up periodically and cause hair loss.