By server management - do you mean VM? Sure, you can outsource that. I mean that what and how a home-grown application uses a database tends to mean that database (software/schema/optimization/whatever) management cannot be application agnostic. So if you outsource this, you're either effectively hiring a consultant that still needs to deal with and learn details of specifically your application, or you should assume it's going to cost you some time to do yourself.
I'm sure you can get advice or buy know-how; but they're too coupled to think you're not also going to need to spend some time too. (At least: assuming your workload is large enough and complicated enough that naive brute force isn't an attractive option).
Everything you are saying is true, but when people talk about managed services, for the most part they are referring to someone else managing the VM, the operating system and the server application running on the VM - in this case the database.
Exactly! That's why I was confused - they didn't replace mongodb with colloquially "hosted" postgres; they stayed at the same level of (partial) hosting. I.e., they didn't "switch to hosted postgres", in any normal sense.
I'm sure you can get advice or buy know-how; but they're too coupled to think you're not also going to need to spend some time too. (At least: assuming your workload is large enough and complicated enough that naive brute force isn't an attractive option).