You have done nothing wrong. VRR is not supported over HDMI 2.1 in AMD drivers because HDMI forum explicitly prohibited AMD to implement open sourced HDMI 2.1 support in their drivers. HDMI forum consider that as breakage of terms of usage and violation of their patents.
Unfortunately, no. DP to HDMI cables rely on a special feature of DP where it can send HDMI signal over DP connector and cable, but, since the driver cannot emit HDMI 2.1 signal, DP will also not be able to send HDMI 2.1 signal.
There is a “kind of solution”. There are active converters of DP signal to HDMI signal. These converters require additional power supply (usually from a USB port). VRR is tricky thou, most of these converters are not able to convert DP to HDMI 2.1 with VRR so you have to search for one that does. Some converters advertise VRR as supported but user experience differ. Try searching for some reviews to find out which converter could likely work for you.
Personally, I have Sony X85J and the same problem and was not able to acquire a converter that proved to be working correctly, thou, availability in my country is poor.
Also keep in mind that converters can introduce a slight latency because they have to actively convert signal from one format to the other.