Okay, with that information and confirmation it supports up to 384 kHz, that confirms with DoP that DAC can only play up to DSD128, and that's exactly what you've experienced so far.
Keep in mind DSD via DoP and DSD via native DSD are two different things that accomplish the same thing. DoP depends on PCM sample rates in order to support higher orders of DSD, e.g. DSD64 via DoP requires the DAC to support a PCM sample rate of 176.4 kHz, DSD128 via DoP requires the DAC to support a PCM sample rate of 352.8 kHz, DSD256 via DoP requires the DAC to support a PCM sample rate of 705.6 kHz and DSD512 via DoP would require the DAC to support a PCM sample rate of 1411.2 kHz.
Since your DAC only supports up to 384 kHz your DAC is limited to DSD128 over DoP. To playback DSD256 and DSD512 you have to disable DoP and use ASIO to output native DSD and make sure DSD bitstreaming is enabled for up to DSD512. You might want to set Output Encoding to None too as dtc also mentioned to test the playback of DSD512. Then look at the audio path (Player menu > Audio Path) to see what's being outputted.
I don't think the documentation is wrong either, it just means that your DAC supports both DSD64 and DSD128 with DoP and native DSD, and DSD256 and DSD512 only with native DSD.