Vivaldi does not Support the opensearch protocol to automatically add new search engines to Vivaldi.
Therefore we need to add a custom search engine, to add our (selfhosted) SearXNG instance, to Vivaldi.
To enable SearXNG as a search engine with working autocompletion you only need these two values:
URL: https://your-searxng.tld/search?q=%s
Suggest URL: https://your-searxng.tld/autocompleter?q=%s
You can now use Vivaldi with your own SearXNG instance.
If you have not yet set up your own SearXNG instance, you can find some publicly accessible instances at searx.space.