Ignoring that Linus himself isn't particularly software freedom-y (I think he, entirely and provably correctly in my view, firmly believes in open source as a way to achieve good software, but the freedom angle isn't as important as for someone like Stallman), Linux being GPL is arguably the reason why it dominates - any changes worth talking about to Linux get propagated publicly and openly, as opposed to if it were under a permissive licence.

Not exactly the same. As I mentioned in the comment, you have direct access to the Linux OS when you host. Open as in access to the underlying OS is open. You can configure it, install packages that you want, etc.

When you run AWS Elasticsearch, you have no access to ES instance. You can't configure it, you can't add your own plugins. You are no longer a user, you are just a consumer of the UI/API, even when the primary product is still called Elasticsearch.

Big difference.

When you run code on a lambda or a serverless VM you never see the OS either.

but that is a feature of their offering. You are comparing apples to oranges here.