Even with the setting to restrict non-logged in users from seeing local and/or remote posts they still have the option to search, leading to results like this
Config options already exist since 3.20. Though it indeed wasn’t mentioned in the cheatsheet yet until just now. Before that, setting the instance to private also blocked search access.
Judging by the screenshot, you’re not on the latest stable release though.
Also note the frontend won’t know about the fine-grained backend settings, only the coarse public/private toggle.