Last week I've successfully brought florian-rappl.de to the cloud - with a migration of the MySQL database to Azure table storage and removing internal services such as the classic ASP.NET (SQL) Memberhip service.
This is only the first step though. In the next step I will actually recreate the whole site as a headless CMS, with the frontend being written from scratch. I don't have a timeline yet, but I am optimistic that I will start (and finish) in this century, maybe even the current decade...
There was a short downtime last week when I missed the removal of my server, however, it was quickly (within 2 hours) resolved. At first I brought the site back online in a readonly mode, then I added a new membership service and write capability on the new database driver. Everything worked.
Since this first step was still a shallow migration (still using .NET 4) I am right now on a quite expensive Windows App Service plan. With the next step I will try to make this a lot more lightweight.