Every time I run FSDT installer, it does an update. (whether files are out of date or not)
That's doesn't have anything to do with how the program works. It's only caused by your local Cloudflare node still not having completed all the synchronization. In fact, it shows the Live Update is *working*, because it KNOWS there's an update to do, but it keeps getting served the wrong file, so it tries again.
In normal times, when all servers are fine, you just click the updater, it will update everything, and if you start it a 2nd time, it won't download anything. That's how it always worked for many months before, and that's how it will work again for you when your node will finally gets all the updates.
And that's why we have an Offline installer to cover precisely this case.