Hello,
Sorry to hear you are having issues. I recognize that you're on Windows 10 Insider preview version. From what I know Stardock do not officially support Insider preview version of Windows 10.

Basj,
Stardock Community Assistant.

Native Windows search still works to find programs as expected, so search indexer doesn't seem to be completely broken, however Start10's connection to it may be. When I look at Indexing Options, I do see entries for Start Menu and Start10Crtrlpnl, so it at least seems set up still. What's weird is, it's only broken for some app shortcuts- unfortunately many that I use often.

My shortcuts are almost universally stored in C:\ProgramData\Microsoft\Windows\Start Menu\Programs

However, I have discovered that the only shortcuts appearing in Start10 seem to be coming from the registry or some other source because, when you open their location, explorer opens to the application install folder, not the shortcuts folder, which would be the normal behavior if the shortcut source were the Start Menu folders.

Rebuilding the search index did not improve the search results.

Setting Start10 to use "Cortana" search instead of built-in does cause the missing programs to be returned in results, but this option suffers from a bug where the first letter typed never registers (the first keypress seems to only initiate the search, but isn't passed the character typed). 

Given the lack of other reports and the inability to reproduce this here it is unlikely any update for Start10 would make a difference.

The most likely explanation based on what we know now is something is broken on your install.  This is why Microsoft say not to use insider builds for production work as they are not ready.

Other products are probably not using the windows search system for looking at shortcuts but instead simply enumerating the shortcuts as they build the all programs list and then searching that internally.

The update that seemed to coincide with Start10 not being able to access search was actually neither, technically. I did an install in place, so Windows retains my application and files but is much more thorough of an install than an update, but resets less things than a clean install.

I understand it's difficult to diagnose something that seems connected to Insider builds, however I'm not sure MS is testing for Start10 compatibility so not sure this will ever be addressed on their end. Since native Windows search works entirely as expected outside the context of Start10 but no one else is reporting/replicating this behavior, I suspect something has broken in my Start10 installation that is not being corrected by an uninstall and purge. I did notice that in the 2 times I used the Purge script, there were still remnants of Start10 left behind in directories, the registry, and the indexer settings. That makes me wonder if enough things have been reset back to a pre-install state before re-installing Start10.