Correct me if I am wrong. But aren't embassies supposed to be sovereign property of the country occupying that ground?
They are, indeed.
Technically, though, the insertion of military forces into another country without their permission would constitute a violation of sovereignty.
Which, in this particular case, amounts to nothing more than a lame excuse. The decision to "approach the Libyan authorities" is the functional equivalent of doing nothing.
Altogether, a horrid decision that no responsible American would have made...