One developer has started a project that created a completely open source code for HDMI output on FPGA devices. This is opposed to using licensed code, or using the DVI protocol over HDMI ports. If you’re looking to create any HDMI-outputting FPGA devices, this might be worth looking at: https://github.com/hdl-util/hdmi/
A note about using HDMI: This code would be free to use on any device such as a DE-10 Nano or other “dev kit”, as you’re buying finished, licensed hardware. That being said, if you’re creating your own products to be sold as a hardware/software bundle, you’ll still have to deal with any potential HDMI licensing issues.