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The question is already in the title: What should I consider when I want to design a PCB with a voltage output up to 2 kV? Only the output lanes are going to be on this level, the other lanes are on 5-10 V.
Can I still use a 4-layer PCB? Should I use special materials, and if yes, which one? The maximum amount of current on the HV lanes is in the nA range, thus not important (afaik).

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The potentially (no pun) biggest problem as I see it is breakdown (or "tracking") of the high voltage across the surface of the PCB and I'd certainly consider making slots in the PCB to make the effective surface distance from HV copper to LV copper as big as you are able.

Then, around sensitive LV circuits (that may be close) to the HV stuff I'd consider a protective grounded guard ring to prevent potential arcing to the LV circuits and their destruction.

It's a dangerous voltage level so keep safe.

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