Godot version:
3.1 dev
Issue description:
It would be good to see a little popup when new version of Godot Engine is released. It should be only shown once when new version comes.

I'd prefer a simple Label that says something like "Update available!", underlined, at the version number and it links to the download page when clicking on it. We have too many popups.
For me the best option, will be add a small bar(like in TV news) at the bottom of the Project Manager.
It should contain the latest news about engine, something like headers from https://godotengine.org/news, and when clicked, they should open a browser with target news
Maybe the bar should move from right to left, like in TV news
I readed #20603, and I think that ideas from this thread, take too much space
Open in new tab to see in full resolution.

Godot doesn't connect to the internet without user intent. At most a "Check for updates" button could be added to demonstrate that intent.
Would an opt-in "Check for updates on startup" setting be acceptable?
The GitHub Releases API may be suitable here, but we'll need to perform some checks to avoid recommending older version patches. For instance, if someone is using 3.1.2, notifying them when 3.2 is released is fine, but they shouldn't be notified if 3.0.7 is released.
Since our Git tags follow the major.minor.patch-stable convention, I suppose this could be handled with relative ease.
Godot displays the version in the corner. Perhaps this could double as a "check for updates" button?
@aaronfranke This would conflict with #35375, unfortunately.
Godot Proposal - https://github.com/godotengine/godot-proposals/issues/1132
Most helpful comment
Godot doesn't connect to the internet without user intent. At most a "Check for updates" button could be added to demonstrate that intent.