recoll is a local search engine based on Xapian:
http://www.lesbonscomptes.com/recoll/

By itself recoll does not offer web or API access,
this can be achieved using recoll-webui:
https://framagit.org/medoc92/recollwebui.git

This engine uses a custom 'files' result template

set `base_url` to the location where recoll-webui can be reached
set `dl_prefix` to a location where the file hierarchy as indexed by recoll can be reached
set `search_dir` to the part of the indexed file hierarchy to be searched, use an empty string to search the entire search domain