My background search engine is set to Google
Have you tried using something else? Google populates its "search engine suggestions" from all the information Google has compiled about you over the years, so perhaps it's just slow at doing that.
Read Customize searching in Safari on Mac - Apple Support. Pay particular attention to the following excerpt (emphasis added):
When you search, you also give information about yourself to the search engine. For example, if you enter “Golden Retriever” in the Smart Search field, the search engine learns that you’re interested in information about Golden Retriever dogs, even if you don’t press Return to submit the search terms. Search engines have different policies for what they do with search data they collect from you.
That passage is included strictly for Google. Every single keypress gets transmitted to them, as you type it. Google calls it their "no return policy" 🙄