Are short links indexed by search engines?
In practice, no. Short links return a redirect (HTTP 301 or 302) rather than a page with content, and major search engines like Google treat the redirect as a hint to index the destination URL instead of the short URL itself. Crawlers follow the redirect and the destination receives the SEO weight.
We don't add explicit noindex headers to short link paths, so the short URL can technically show up in search results if a crawlable page links to it directly. But because there's no body content to index — just a redirect response — this is rare in practice, and clicks on those results will land on the destination URL anyway.