Not sure if this a bug or a feature request, but URL rewrite rules for reddit.com should apply to the Reddit comments button below search results. If you use them to redirect to old Reddit, the button will still open the new version.
A search that triggers this button: https://kagi.com/search?q=copilot+key&r=no_region&sh=Bw3U3kFV2pLvfAYXDzPsSw
The button should apply the redirect rules like they are for normal results.