I would also like to find documentation stating Microsoft intentionally did not include file explorer search history in Windows 11.
Changing the default for displaying recent search entries to off is somewhat understandable.
Removing the option and not allowing user control of that feature is not understandable.
I found a YouTube video 'How to Disable File Explorer Search History in Windows 11' thinking if you can disable it, surely you can enable it. Following the video, I used gpedit.msc to get to the File Explorer, Windows Components settings for 'Turn off display of recent search entries in the File Explorer search box'. Available options are: Not Configured, Enabled, Disabled.
My setting was "Not Configured".
Setting to 'Disabled' did not resolve the problem.
Setting to 'Enabled' then 'Disabled' (again) did not resolve the problem.
Note: The settings window shows "Supported on: At least Windows Server 2008 R2 or Windows 7".