Vlad SearchPreview maintains a snapshot of sites and I don't believe they get updated unless someone specifically requests they do. For me that's enough, I'm able to sift through websites quickly when searching for something very niche or specific.
However, I understand if crawling pages to generate and store snapshot images is a bit much to ask.
SearchPreview support for Kagi is likely the easiest solution but that might be a bit complicated right now at least due to Kagi being in beta.
If this is something unviable for Kagi to implement I'll start a dialog with the extension author.