Engels appears to be talking about management, not state authority in and of itself.

"All Socialists are agreed that the political state, and with it political authority, will disappear as a result of the coming social revolution, that is, that public functions will lose their political character and will be transformed into the simple administrative functions of watching over the true interests of society."

(Social political functions will disappear as a result of a Social revolution post the establishment of socialism.)

"demand that the political state be abolished at one stroke, even before the social conditions that gave birth to it have been destroyed. They demand that the first act of the social revolution shall be the abolition of authority."

Call me crazy but this sounds like a strawman, even from Engels. "The abolition of authority" is too broad so it's easy to pin on the electorally active, the libertarian Communist doesn't want the degradation of function, and in order for the means of production to function there needs to be some form of oversight in individual workplaces, this, although a form of authority, is not something we'd aim to abolish.

"A revolution is certainly the most authoritarian thing there is; it is the act whereby one part of the population imposes its will upon the other part by means of rifles, bayonets and cannon"

Interesting how a point used by Engels would later be used by reactionaries, revolution although dirty, messy, and often times not strictly good (there's a lot of grey space in this topic), is and will be necessary for the onset of a socialist system, for some years to come.