Shinjuku to Nikko

Hi everyone,

I'm planning a trip using the JR Pass and need some clarification on the surcharge for the Shinjuku to Tobu Nikko direct route. My understanding is that the JR Pass only partially covers this journey since the train travels partly on Tobu Railway tracks. I've read that the full fare for this direct train is approximately 4,000 yen, but with the JR Pass, there's a required supplementary fee of about 1,560 yen. Can anyone confirm if this is accurate? Additionally, does anyone know the current process for paying this surcharge at the station?

Thanks in advance for your help!