It is more nuanced: Dart on the server side is supported, but the development focus is on the client-side stories (Flutter and Angular).
Google's Dart team develops e.g. the Dart VM which is great for server workloads too, they do provide some server-side libraries, but they themselves don't work on third-party database drivers (for now).
Think of it as the question of focus: they want to focus on the client-side story, get it right, and then deal with the rest. Spreading thin won't help either.
To me , dart on the server , with their agent / isolate based concurrency as well as async await language support, provides ( in theory ) one of the most exciting environment to develop backends on.
But Google's Dart team is not actively involved in developing e.g. the Postgres driver, it is done by an independent company who is building their stack on server-side Dart.
Btw. I agree: the isolate-based concurrency + language tools is really great for server-side Dart apps. I use it in a highly concurrent data setup, and I wouldn't switch to other language.
From Google's point of view, we would all be using it.
What gives you that idea? The Dart VM is listed on the platform page for command line and server side programs. https://www.dartlang.org/guides/platforms
The focus of Dart 2 and beyond is the client side [0].
You can definitely run Dart in the VM, but beyond the HttpServer API, server-side support is mostly a community effort.
My point isn't that this is a bad thing, it's that it makes sense for Firebase to be promoted because Dart doesn't have _official_ server-side support.
[0]: https://medium.com/dartlang/announcing-dart-2-80ba01f43b6
Analogy: JavaScript is focused on the client too, but people also use it on the server.
I do agree they have pivoted to a more client-sided branding though.
But it actually makes sense on a closer look. Dart on the server is not officially supported, as the primary focus of Dart is use as a client-side language, so it would be a bit confusing for the Flutter documentation to recommend using Dart for a backend.
That being said, I think Flutter is a great platform for quickly building apps, and getting consistent behavior across different vendors. I think that it can only continue to get better.