Both AWS and Azure support Oracle Databases. This is the selection of a cloud provider, not specific software that would run on that provider. They may very well run Oracle Databases in the future.
That may be the case but as my employer is learning it takes a ton of engineering effort to actually run a complicated, large scale oracle DB on the cloud. At every turn you either have to compromise on design or expend a ton of effort getting over the hurdle. Even at large scale running it bare metal and then distributing that around the world is easier (that's what we've been doing). Time will tell if the effort is worth it.
I’m a cloud True Believer but even I wouldn’t suggest it is the right choice to run any large third party proprietary database like SQL Server or Oracle on AWS.
At least with AWS’s custom Aurora/MySQL and Aurora/Postgres offering they are able to rewrite parts of it to take advantage of their other technologies, but when you look at their RDS offerings, it doesn’t really buy you as much if you need to run third party commercial databases at scale.
We built software for data analysis for the government and had to integrate with their data storage systems. I wasn't exaggerating when I said they loved Oracle. In my experience, they seemed to think Oracle databases were superior in almost every way.