HDMI to DVI with this resolution does not work without an active converter. The adapter cables are all passive single-link cables, regardless of whether they have 24+1 pins or not, because they only transmit the HDMI signal to 1 link - so 1920x1080 is the highest resolution you can get with 60Hz. If you lower it to 30Hz (if necessary with CRU), it should work with 2560x1600.
Since your notebook has USB-C with DP/Alt mode, I would try this: Delock USB-C to DVI-D (1m, USB C, DVI) - this converts the signal directly, thanks to USB-C power supply, nicely compact in 1 cable.
I haven't tried it with a 4B model yet, as I don't have one at hand, but I bought the cable for exactly this purpose and have used it with various Raspberry 2 and 3 models. I would be surprised if it didn't work with the 4B model.
Yes, I have used the cable for a connection from the PC (HDMI) to the monitor (DVI) and it works fine. I cannot say whether it also transmits audio signals, as I use an external speaker.