After this, I close FSDT Installer and was able to then launch it again. So looks like running the Offline Installer once fixed the issue
If this was fixed that way, the most likely causes were probably:
1) your antivirus/firewall blocking the Live Update but not the Offline installer.
That's because the offline installer, being "offline", doesn't download anything, so it's less likely to trigger antivirus heuristics that, instead of trusting a digital signature as they are supposed to, it prefers to rely on unreliable behavior pattern like "it's downloading something, it might be dangerous"
2) your local cloudflare node not updated to the latest version.
Both issues are the reason why an offline installer exists but, something like not even starting, it's more likely issue #1 because even if you didn't get the very latest updater, the previous one surely worked so, it's more likely it was prevented to start.