As I mentioned, Microsoft changed the code to display results-as-you-type. The old code that waits for you to press Enter before starting the search is also the code that includes the history feature.
The equivalent results-as-you-type code in Windows 10 keeps only three items in its history and that's based on clicking somewhere outside of the search box. That is, if you were to type "cat" and wait for results and then backspace and type "dog" and wait for results, neither would go into the history at that point. As soon as you click outside of the search box, "dog" would be added to the history, but not "cat". That's a reasonably good design and doesn't have to be limited to 3 items.
FYI, Windows 10 had the wait-for-Enter style search with history from 2019 to 2023. Windows 10 was reverted back to the old results-as-you-type code with only three history items at the end of 2023. That change was a side effect of Microsoft complying with EU requirements to decouple Bing from Windows search. It's likely the same reason the Explorer search changed to results-as-you-type on Windows 11, but for whatever reason, it got implemented even more dumbed down with zero history.
Privacy is not an issue. The Explorer search history is specific to your user profile. It's no more an issue than browser history or the files you save in Documents. It's all connected to one user account. It's just an implementation detail that we'd like to see addressed.