SUMMARY Practically in all video players and websites, the user sees a "pause" button when the video is playing, and vice versa. Although these icons in Breeze are for "status", not buttons, so they are literally "correct". But the user is likely to be accustomed to the above patterns, so it might make sense to switch these two group of icons. It seems only Breeze provides these status icons. Adwaita only has -pause and -start action icons. So changing this is unlikely to affect anything but Plasma.
If only media playback gets inversed but nightlight, audio etc.. icons stay the same, wouldn't this be even more confusing? (Assuming you are talking about the system tray icons)
As you mentioned, status icons are meant to show status, so the current icons are objectively correct as status icons. In the video players and websites, the user sees a pause button when the video is playing because the button is a clickable action button; you left-click on it and it pauses the video. So the icon and text are telling you what *will* happen when the button is pressed. In the Media Player widget--which is where people complain about this--the icons are indeed being used as status icons and not action buttons; you can't left-click on them to play and pause the video or audio. As such, they're being used correctly and no change is needed.