I'll look into how this can be solved, but the registry keys were removed to avoid Origin Client forcibly updating the game to its own version.

fix is simple - you need to edit registry key:
HKLM/SOFTWARE/(Wow6432Node*)/BioWare/Dragon Age
rename value 'Path_' to 'Path'

if you have DAO installed and Path points to the correct folder, Toolset will install.
If you use Origin Client and don't want it to update the game automatically, you need to rename the value back after installation.
If toolset cannot find the game after install, run toolset configuration and point it to the game folder. It will work afterwards.

* on 64bit OS

run the launcher / or config tool at least once - you will have the path entry.
Hotfix removes current key and modifies files to write a Path_ value instead of Path

For them it is a feature, most certainly not a bug. It works as intended from their side.

Currently I suspect there are some problems with Galaxy Client and the newest Windows 10 update. Keys / shortcuts are not being created.

If you installed the game via Galaxy Client, try Verify / Repair option - this should recreate the keys.
If you used offline installers, you can create the key on your own
- right-click on BioWare key, choose New -> Key, name it Dragon Age
- click once to highlight the newly created key, right click again, New -> String Value
- name it Path, it should appear in the right panel
- double click the new value and a window will appear where you should put the whole path to your installation

Please do, although you might have to wait for a response till morning (it's around 1AM here now ;) )