Safari won't play videos (macOS Sonoma 14.3)

For a few months now I haven't been able to play videos in Safari. Clicking play on any video just displays a still frame, even as the video's timestamp advances and I can scrub throughout the video to any frame.

I resolved it once by clearing the cache, but before long the issue returned. It's also odd because the issue persists even in a private browser, suggesting that it's not actually a problem with the cache.

Anyone else have this issue in Sonoma 14.3? Any suggestions?