I have that same adapter
Problem is/was, it worked the first time I tried it (about two months ago) with an iPad 12.9 and Duet, but then it started behaving badly (with both the 10.5 and 12.9; glitchy performance, resolution problems, and this rather bizarre pop-up showing me how to activate Airplay, which is apparently needed). At that time Duet wasn't working at all without this adapter, so that's why I bought it.
It was wonky with this adapter, but maybe they fixed it with an update to Duet (which is not meant to run with any adapter, so who knows). The adapter did sort of fix it (for a while).
The problem was, Apple surprised everyone with some major changes to Airplay (without any warning fo some), with has caused all sorts of problems. This was a quite a while ago (don't hold me to any of this, i'm guessing, partially)
The Luna option at least has support with the software/ hardware solution. And it's USB-C, so you can avoid a dongle.
Should be $50