A search engine takes a query and returns ranked results, sometimes with advertising, maps or an AI assistant on top. Organisations meet the category in three ways: as the default engine in staff browsers, as embedded site search on their own websites, and as a search API that feeds research tools, products or AI applications.
The sovereignty question sits in the index and the ranking. Some alternatives to Google Search or Bing combine their own crawling with results from partner indexes, so a provider can be European and still depend on a non-EU source for what you see. The Digital Markets Act places extra obligations on the largest platforms, including online search engines, but it does not tell you where an individual query is processed or what is stored alongside it.
When choosing a European option, ask whether it runs its own index or relies on partners, which ones, and how queries are passed on. Check whether IP addresses and queries are stored or linked to an account, how the service is financed, and whether its retention practices are published.