Flyout: make it obvious there are features inside it

[humitos]

The logo takes up a lot of space and doesn't exactly communicate "click here for hosted features".

(@agjohnson in #360 (comment))

I agree that the logo would benefit from some change. The current state looks more like an advertisement for RTD than a feature of the opened project’s docs; this disturbs users' focus.

(@orangesunny in #360 (comment))

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I'm opening this issue here to talk more about this and find a way to keep the Read the Docs branding on the flyout while communicating there are hosting features behind a click on the it.

There is an issue opened about re-designing the flyout completely as well at #53

[agjohnson]

It's also worth mentioning that we lost the dropdown caret in this version of the flyout. Without this visual clue, it's not clear the menu even expands:

I think the collapsed menu is not the best place to advertise RTD -- at very least for our full wordmark and logo combo. The user hasn't interacted with any features yet, which makes the full logo and wordmark on the flyout feel more like subtle brand placement than a feature users should interact with.

I think a solution is to move our full branding into the flyout, where the reader is interacting with our features. This leaves the most valuable real estate, the collapsed menu, open for features the reader/maintainers need. We're limited on how big we can make the flyout before it will become a nuisance.