I don't think that is your search history, this looks similar to the suggestions you see on various online search pages like Google that show popular suggestions based on what you type in the search bar.
I don't know if you can disable this feature for the Windows search bar.

Click in the field, enter a character or two and STOP ! Using the arrow keys, highlight an unwanted entry. Then press Shift > Delete Repeat as needed.

Hi dictator, I think that is the same list of Frequent Sites you would see on the "Jump List" displayed when you right-click the Firefox icon on the Taskbar. Firefox has some preferences for the Jump List, but if you hide the Frequent list then the Jump List shows the Recent list, which may be worse. Hmm.

Note that for the jump list you have these prefs on the about:config page.

browser.taskbar.lists.frequent.enabled
browser.taskbar.lists.recent.enabled
browser.taskbar.lists.tasks.enabled

• https://support.mozilla.org/en-US/kb/about-config-editor-firefox