MarginaliaSearch
Website owners can choose an immediate full recrawl of their already indexed website
If you have an RSS or Atom feed the search engine should update automatically within a day or so of the new entries. This is not a full recrawl, but will only add the updated documents.
Manual triggering of updates is a harder problem that requires website owners to somehow be able to prove that they own the website.
You could ask the website owner to put some code or link in their website. For instance you ask them to put <!-- Marginalia user: 0x333 --> in the root of their website. Then they will have access to request re-crawl.
However, there is one thing I'm unsure about. Is it better to make it a component outside Marginalia? Or integrate it with Marginalia? In the former case, other instance admins could simply not include this component if they don't need it. The latter case, it is probably easier to implement and integrate with Marginalia.