Splitting this out from #467

In the current plugin implementation, the Editor screen has no headings at all.

It misses a main H1 and maybe it could benefit from some H2 used to identify the main UI sections (to evaluate, this depends on the actual grouping of the main controls).

Headings are used for content navigation and allow screen reader users to "jump" from a section to another one. That's clearly explained on https://make.wordpress.org/core/2015/10/28/headings-hierarchy-changes-in-the-admin-screens/ which also illustrates all the work done about headings in the last releases.
A proper headings hierarchy is also a WCAG requirement.

I'm not a designer, so I'd leave the visual part to designers 🙂 For the accessibility part, I'd propose to discuss this issue in the next accessibility meeting on Slack.