The warning message is not present in the beginning of editing.

Wouldn't really help, a user can get logged out mid-editing just as easily, and we probably don't want to continuously poll whether the user is logged in.

When a logged-out user attempts to save an edit

• the displayed warning message does not communicate clearly what exactly happen (the language of the warning is too technical)
• does not provide any info to a user what options a user has for editing (log in again or publish as anon edit).

Any text suggestions? Should it maybe include a login link that opens in a new tab? (Does that help more than it confuses on mobile?)

Both, VE and wikitext editor do a good job to communicate to users what happened and what next steps might be:

But they provide a "try again" option, and we don't (at least in the current minimalistic implementation).

Come to think about it, the recent patch actually makes it impossible to save your post under a different username from how you started it. Not sure what to do about that...

If a logged-out user confused by "Assertion that the user is logged in failed" message would change the editor (to VE or wikitext) even more enigmatic message will be displayed:

As in, this error is shown when you switch editors? (And prevents the switch?) That ideally should not happen, not sure how easy it is to isolate that code path though.

Unnecessary confirmation dialog box if a user decides to cancel their edits:

Why would that be more unnecessary than showing that dialog on cancel in general?