I believe those message comes from the gifski renderer and looking at the code, progress is activated in interactive() session.
There does not seem to be a way to deactivate the progress with this renderer.
One solution would be to render your document in a non interactive session. When I click on the knit button in RStudio, it renders in its own session and I don't see any progress in the resulting html.
Also, about the option, as the progress is printed without using message or warning, the knitr option are not useful I think.
Another solution maybe changing the renderer in gganimate. magick instead of giski ?