[chrissix666]

When using the context menu item "Manage -> AB: Choose Artwork" for TV shows or movies, and then selecting a new image, say "poster.jpg", Artwork Beef is not replacing the existing poster.jpg, but instead creates poster1.jpg, poster2.jpg, etc, etc. files which are not desired. Also, since Kodi only recognizes "poster.jpg" files for that art type, the new files are ignored, and the artwork in Kodi not updated. Is this as intended?

For me, the sole reason to use this feature, is to replace (existing) artwork I do not like, with alternatives. So with that in mind, I absolutely want AB to overwrite the existing file. Just to clarify, this is not due to permissions issues (as far as I can tell).

Sure it does! All working fine!
You have to unselect the current local art on first place on top, and select the new art you want. Then it will be exchanges as desired.

If you don't unselect the local art on first place on top and only select new ones they will be downloaded as poster1, poster2 ...
AB context menu behavior changes since a few versions ago.