It shared out as a pro res .mov file because you chose the Best quality option when sharing out. All other share options would have yielded an H.264, Mp4 file. Pro res is a very high quality, high bitrate, high file size codec. But it is not the HEVC codec so that confirms that a shared out HEVC movie does not retain the HEVC codec.
Thanks for taking the time to do the experiment and reporting back your finding.
You can do a screen shot by simultaneously pressing Command>Shift>4, and that will morph your cursor into a cross-hair. Then with your trackpad or mouse, press-drag the morphed cursor over the screen to outline the area that you want to select, and release. That will give you a screen shot on your desktop of the area that you selected. If you want a shot of the whole screen, press Command>Shift>3. No need to outline anything. The screen shot will automatically be taken.
Cheers,
Rich