I'VE GOT THE SOLUTION – but it may not work for everybody.
Okay Gang,
This issue has been a problem since May 29, 2022 when Keynote 12.1 was introduced or when it was updated on June 21, 2022. I know this because my wife's iMac is running 12.1 and the video export is screwed up there too, although not quite as screwed up as 13.0.
I never encountered the problem because I was using an older iMac which was running Keynote 11.0.1, and my older MacBook Pro was using Keynote 11.1. When I bought my new iMac, it came with 13.0 and suddenly I was stuck with the problem all of you are experiencing.
But I found a solution and it took me about three minutes to fix the problem.
It made sense to me that if I could install a previous version of Keynote, specifically 11.0 or 11.0.1, that would fix the problem. But I was talking to an Apple Advisor this morning and he said that wasn't possible. I thought he was wrong... and in fact, he was wrong.
After a search I found this site: https://www.inkppt.com/post/install-previous-version-keynote
It was created by a brilliant young man named Abhijeet Kumar, who is a student at The Pennsylvania State University: https://www.linkedin.com/in/abhijeeetkumar/ I'm now following Abjijeet on LinkedIn.
What Abhijeet's solution requires is for you to have access to an older iMac or laptop that is still running 11.0. Fortunately, I'm always slow to update applications, so both of my other Macs were running versions of Keynote 11.
As I said, it took about three minutes to install the old version from my MacBook onto my new iMac and to toss 13.0 into the trash. [Note: Abhijeet grew up in India where they refer to the "trash," as the "bin." So you will see "bin" in his instructions on getting rid of 13.0.]
So now on my new iMac I'm running Keynote 11.0.1 which was created in 2021 and last modified on March 30, 2021 and it works perfectly.
Shame on Apple's Keynote team for not correcting this issue three years ago when it popped up.
Best of luck to all of you!
Sincerely