Same issue here, despite Couatl64_MSFS is running in the Task Manager.
If it's just stuck, it's 100% a server problem. As you might now, we use Cloudflare to prevent the usual "site going down the release day", which happened to every other major release. Because of the Cloudflare network of 260 nodes spread around the world, we don't risk having the server put down, so NOBODY could download anything.
The side effect of this, is that it takes a few hours for all nodes to get all the current files, and this time we updated A LOT of files so, if you run the FSDT Live Update again, all right files will eventually be up.
A crucial file that, it not updated, will stop the program from working, is this one:
http://update.virtualisoftware.com/setup/fsdtroot/couatl64/bglmanx_fsdt.datIf you can't get the latest version through the updater, because your Cloudflare node still has the previous version, downloading it from here should fix the problem. The file you downloaded MUST be placed in the following folder:
Addon Manager\couatl64
And overwrite the file with the same name which is already there. This should get you going, until the servers catch up.