I was finally able to deploy this easily without hacking on Turris Omnia’s OpenWRT and test if it is working correctly.
It’s not rocket science, you just need to make sure you have the latest OpenWRT and follow these instructions. I hope there will be a GUI setting in the interface in the future.
Whether you have it on your computer or on your router or on both (my preferred option), you can test if it is working correctly on a service called dnsleaktest.
Have fun and stay safe and private!