Stop File Explorer remembering your searches — via Microsoft Learn

Group Policy

Open gpedit.msc (Pro, Enterprise and Education only) and go to:

User Configuration > Administrative Templates > Windows Components > File Explorer > Turn off display of recent search entries in the File Explorer search box

Registry equivalent

Double-click a .reg file and confirm to merge it. Right-click → Edit first if you want to read it, which is always a good idea with any .reg file from the internet.

Apply

Windows Registry Editor Version 5.00

; Oddbyte.Me: Stop File Explorer remembering your searches

[HKEY_CURRENT_USER\Software\Policies\Microsoft\Windows\Explorer]
"DisableSearchBoxSuggestions"=dword:00000001

Undo

Windows Registry Editor Version 5.00

; Oddbyte.Me: undo Stop File Explorer remembering your searches

[HKEY_CURRENT_USER\Software\Policies\Microsoft\Windows\Explorer]
"DisableSearchBoxSuggestions"=-

Same thing from a command prompt

Run in a normal (non-admin) Command Prompt or Terminal.

reg add "HKCU\Software\Policies\Microsoft\Windows\Explorer" /v "DisableSearchBoxSuggestions" /t REG_DWORD /d 1 /f

Undo:

reg delete "HKCU\Software\Policies\Microsoft\Windows\Explorer" /v "DisableSearchBoxSuggestions" /f

Many tweak lists present this value as a way to remove Bing/web results from Start search. Microsoft's documentation only describes the File Explorer search box behaviour, so don't count on it for Start.