For results that are a YouTube result, in my opinion it'd be great if Kagi offered users the option to watch the video embedded on the Kagi page, using Google's most strict privacy settings for embedding.

There is a certain competitor that already does this. Their documentation for the feature: https://duckduckgo.com/duckduckgo-help-pages/duck-player
Google's docs for youtube-nocookie embedding mode ('privacy enhanced mode'): https://support.google.com/youtube/answer/171780?hl=en#zippy=%2Cturn-on-privacy-enhanced-mode
Note: I realise this seems a lot like thread 6184, but the privacy aspect is the crucial differentiator here, in my opinion.