My suspicion is that this problem is with the Android OS, not the Windows App, which is why Microsoft is quiet about it.
Before trying the Your Phone app, I tried PushBullet, which is a non-microsoft product. It has similar features, where you can text from your desktop, etc.
It exhibited the same spurious duplicate text issues. In fact, those duplicate text issues were why I uninstalled Pushbullet and tried "Your Phone" in the first place.
I suspect that the reason some of those other apps worked (ie: samsung flow, google messages, etc) is because they install a replacement messaging app, which is tightly integrated with their PC messaging client.
In the case of PushBullet and "Your Phone", they just try and piggy-back onto whatever existing messaging app is there, using the core OS facilities for doing so, and that's where the issues arise.
Just my two cents.