Do you mean the Webflow search results page?
IIRC indexing occurs 2 times a week on CMS plan, and once every 24h on business plan. I’m not sure how quickly a manual indexing request takes.
I’ve not tested how Webflow’s search engine integration works with markdown excerpts, but it would be indexing the content directly, not the javascript-rendered HTML table.
Webflow search might possibly ignore Embeds altogether no matter what the content is, there isn’t much documentation I’ve found on its implementation.