I have seen the same issue (Macbook air M1, Lightroom Classic version: 10.3 [ 202105281559-8dc50eb4 ]). This is what I found:
When I exported images to slide show where the images reside on an external HDD, the export task stalled again and again. Restarting LrC did not help.
When I moved the same images to the main drive, imported the pictures from there, the export slideshow process succeeded 100% every time.
The target directory was always my home directory.
This is repeatable on my machine, I have done this a number of times now, with the same results: Slideshow exports when images reside on external HDD stall, while slideshow exports when images reside on he main drive succeed.
It's incredibly frustrating to have to move the pictures from one drive to another in order for this to work. I would like to see this work independent of where the pictures reside.