So, if that can help someone facing the same issue... I don't have the answer why it didn't work when running the Hybrid Wizard from the Exchange Servers (Windows 2012 R2 updated to the latest update).
But installing the Wizard on another VM with Windows 2019 worked. I don't know what to get from that, but for me it's enough... I can now proceed with the migration and I'll be happy to get rid of those Exchange servers.
Thanks!