I had a paralyzing fear of public speaking which I have now mostly overcome. However this was almost entirely anticipatory fear that would go away once I actually started to speak, for example I would lose sleep about teaching a small group, excessively rehearse even for small and relatively unimportant public speaking occasions. My worries were mainly related to performance failure, e.g. that I would lose track of my plan, that I would stammer too badly, that I would suffer momentary anomia and be unable to get past it, or that I would freeze in some other way.

Audience engagement: entirely orthogonal to fear of public speaking at least for me. I may be self-critical later on if the audience isn't engaged, and may try to adapt on the fly if I notice signs of reduced engagement, but for me the fear is gone as soon as I start talking.