Exactly the same issue...
I'll try to track you ;)
Actually, although a couple of days has already passed since I had installed the Windows 10 Anniversary Update (officially, i.e., no Windows Insider ring), my Gadgets app version is stuck at 4.3.10820.0, like mentioned by other forum participants, whereas all other Store apps are, apparently, constantly updated to the most recent version. My Windows 10 Anniversary Update is also the stable release build 10.0.14393.67 (US language and region), but my Microsoft Lumia 950 XL firmware (released on July 1, 2016 and branded TMO, as I am currently in the EU) is allegedly newer than that of most commentators: 01078.00053.16236.35022.
Obviously, such an unusual Gadgets app behavior prevents the users from updating the Microsoft Display Dock HD-500 firmware, etc., as the dock simply remains unrecognized (although a connection signal is always audible and the Continuum portion functions as predicted via HDMI screen).
Various Internet posts (in German) specify that the Gadgets app has indeed received an update to version 4.4.1607.11000 4.3.1607.5001 for some users automatically two days after the Windows 10 Anniversary Update installation; however, this is obviously not the case here... What is the problem, Microsoft, that the user experiences differ so drastically, even if the completely identical smartphone models and/or even the same language and region settings are concerned? As I would try to avoid joining the Windows Insider's rings (e.g., Fast) unnecessarily, somebody help! Any communal and/or Microsoft's assistance would be highly appreciated.