Following on from your annoyances and discoveries (to which I agree) I have submitted Apple Feedback FB10011828 regarding the Save As... dialog in Safari:
"For most apps, the “Save As…” dialog includes the ability to set or not set the “Hide Extension” flag for the file being saved. See attachment 1 for Text Edit’s “Save As…” which has the expected drop down to enable or clear the Hide Extension. Setting or clearing this flag remains sticky for future saves until there is a need to change it.
For Safari, the “Save As…” dialog does NOT include the ability to set or not set the “Hide Extension” flag for the file being saved. See attachment 2 where the drop down does NOT have the item which enables or clears the Hide Extension. In practice, the file is always saved with the Hide Extension flag off.
Safari should behave like Text Edit and does not. Most 3rd-party apps (there are some exceptions) have been updated to use this method of setting the Hide Extension flag. I believe this was introduced with Mojave.
This misbehaviour is certainly present in Safari for macOS 12.4 betas and 12.3.1. I suspect it has been present since Mojave, but have not tested that.
References to this issue (which you can ignore):
https://forums.macrumors.com/thread...tomatically-being-added-to-file-name.2344035/ As is the nature of forums, the thread is somewhat confused - but it does highlight that this is an issue for others.
https://discussions.apple.com/thread/250107448 where the change in behaviours between HS and Mojave is described (without reference to Safari)."
And there were the 2 obvious screen shots with which I won't clutter this post.
If I get any response, I will let you know.
You really went above and beyond. Thanks very much for your time and effort. Greatly appreciated.