Well, I investigated HDMI/DVI stuff a bit. For 720x576x50 progressive video mode, which works perfectly via analog VGA, the calculations doesn't look optimistic. Pixel rate in this mode is 27MHz which means bit rate 270MHz. To implement it in this project I have to do the following:

1. Overclock rp2350b deep enough to handle 270MHz bit rate. It looks possible. At least there are a lot of projects doing this, especially for HDMI/DVI support.
2. Recalculate some timings and delays in existing software. Not a big deal.
3. Implement the functionality itself to support DVI. This is the challenge. However, there are successful implementations can be found in the net.

The real obstacle to move forward with this implementation is probably current PCB design. I'm not sure if it will work for 270MHz bit rate. First of all, rp2350b is located on WeAct board which connected to PCB with a connector. Then HDMI and VGA networks are messed up a bit on the PCB itself. Unfortunately, I didn't take into account DVI timings when designed the PCB.

For now it looks like there is no sense to even try implementing HDMI/DVI output with the current schematic and design.