Creating a pre-recorded lecture

If you don't mind skipping your own face, your easiest, cheapest option is probably PowerPoint itself. PowerPoint allows you to record audio (and animations) for each slide, set up timing for the next slide to start automatically, and export the entire thing as a video.

I'm not aware of any product that both fits criteria 1 (free) and criteria 3 (video of you).

OBS Studio fills your description.

It is not the easiest program to use, but you can find plenty of tutorials on YouTube.

While rewinding the recording again might seem appealing, it is very common to find out more errors after you complete the recording. In that case, you need a better video editor. OBS studio might be enough, but shotcut is your best bet.

If we look at the world of movies. We see that long single takes (cut less scenes) are rear and often talked about. There are hard to do, and slow down the pace of a movie. Consider recording in smaller slices.

Next consider that mistakes can improve teaching. If you show your students that you also make mistakes, then you can improve their confidence. When I teach the same class over and over, I get good at it. When doing demonstrations, I have to concisely add in mistakes. I am demonstrating how to program. If I show that I get it correct first time, then I am not showing right.

For high-stakes presentations, I suggest writing a script. 1 page of well-spaced A4 reads back at ~3 minutes and allows you to get your points across clearly and concisely, especially points that need to be well-phrased.

This should enable you to do a one-take presentation on Zoom or OBS.

If you baulk at writing a presentation, record yourself, transcribe it (I think that’s built into Word on a Mac) then tidy it up. If you are like me, that will involve deleting many instances of the word “arm”.