Here's a screenshot of the Search pane in the Preferences window of Safari 16 on macOS Big Sur. (This was before Preferences became Settings in macOS.) Note that the preference "Include search engine suggestions" is clearly associated with the "Search engine" preference.
Safari 17 (on macOS Monterey and later) added separate settings for search engines in private and non-private windows, as seen below.
However, Safari 17 didn't add separate settings for "Include search engine suggestions" in private and non-private windows. The resulting user interface is confusing, even misleading. Despite the vertical proximity of the "Include search engine suggestions" setting to the "Private Browsing search engine" setting, and the vertical space separating them from the (non-private) "Search engine" setting, it turns out that "Include search engine suggestions" governs both private and non-private search engines. Worse, the text below the "Include search engine suggestions" settings implies that it applies only to the private browsing search engine.
Private Browsing uses on-device information to provide search suggestions. No data is shared with the service provider.
Yet data is shared with the search provider, Google in this case, when you type in the address bar of a non-private Safari window with "Include search engine suggestions" enabled. If you have a network extension installed such as Little Snitch, you can see how your every keypress triggers a Safari connection to the clients1.google.com domain.
The grouping and vertical spacing of the user interface items in the Safari Search pane don't properly reflect how the settings work. It looks like a copy and paste job, where the search engine setting was merely duplicated without giving much thought to the consequences.
This type of faulty design and lack of attention by developers is unfortunately endemic to Apple nowadays and reflective of its current culture. The corporation has become a pale imitation of its former self, once famous for sweating every minor detail.
By the way, while we're talking about the Safari Search pane, I would remind you to disable the "Preload Top Hit in the background" setting.