Have you looked at the OpenSearch Description file for your instance? It might be generated with an IP by SearXNG not knowing the hostname. The URL is probably https://search.home/opensearch.xml
.
If you want to examine the search engines in your browser profile, they're stored in a json file compressed with a mozilla specific variant of lz4. The file is search.json.mozlz4
and can be unpacked to json with lz4json.