My assumption is that they are recorded locally, then hashed, then the hash is sent to Azure (Microsoft cloud) as Windows Hello leverages some cloud features. Some things in Azure have warnings about taking up to 24 hours to take effect.
Hashing locally and sending the hash to a server is the same way all passwords for online services and systems work, so nothing nefarious there.
There's probably perceptual hashing so they can count 95% similarity as a match without having to check against the source material every time.