Firefox can do the trick by using Smart Bookmarks Folders.
If you want to use Chrome URLs itself, there does not seem to be anything relevant. This is because Firefox handles bookmarks and history not via Chrome URLs, but via Places.
What are Smart Bookmarks Folders
This feature is made available since Firefox 3 was released in 2008 back then. Ten years later in 2018, probably remain less known to the end users except for this article on Firefox Help, which does not explain much by itself: Restore the default Smart Bookmarks Folders.
The MozillaWiki has the useful information:
Places is currently enabled for Firefox 3 and greater, powering History and Bookmarks, as well as providing plumbing for Livemarks, Annotations and Microsummaries and the Awesomebar.
-- From Places on MozillaWiki
Places is designed to be a robust back-end for Bookmarks, History and related components using the mozStorage wrapper for SQLite.
-- From Places:Design on MozillaWiki
Create a Smart Bookmarks Folder
The early documentation of Places could be traced back to this 2008-dated thread on mozillaZine Forums, whose title "Places query syntax" had quoted "Places query URIs" in the references. In the latter, places
URI that enables the Smart Bookmarks Folder is explained:
You can use a place
URI as a bookmark. For example, if you right-click on the toolbar and choose "New Bookmark," you can enter a place
URI there to create a new query on your toolbar that, when clicked, will reveal a popup containing the results of the query.
One thing that the documentation did not mention is that "reloading" is required to take effect. Therefore:
- When creating from Bookmarks Toolbar, user will need to hide and unhide toolbar or,
- When creating from Library (shown as "Show All Bookmarks" in menu bar or menu button), user will need to close and reopen the window
This is a better way: Open Library via Chrome URL and reload quickly with one press of key (explained later at below).
Anyway, the created bookmark will auto-magically transform into a Smart Bookmarks Folder. Once transformed, user can not edit the same bookmark again. So instead of editing the same bookmark, user will have to create a new bookmark again to use other parameters as user wish.
Create bookmark for search history
Finally, to the point. To create a bookmark for searched history in Firefox, do the following.
Type Chrome URL of Library and press Enter.
chrome://browser/content/places/places.xul
In the sidebar, go to All Bookmarks > Bookmarks Toolbar (or similar location of choice), then create a New Bookmark.
Fill in the Name and Location with string of choice.
Name: History Search 'time'
Location: place:queryType=0&terms=time
Click Add to finish.
Press F5 to reload Library, then go to the created bookmark.
Following above steps, and perhaps after searching "time" at several sites later, the result is shown in the screenshot at below.
![Searched history in Firefox using Smart Bookmarks Folder](https://cdn.statically.io/img/i.sstatic.net/o7ANy.png)
By the way, the searched history using Chrome URL shown by OP does not seem to work in some Chrome-based browsers such as Opera and Vivaldi. The searched history in Firefox is made possible by using Smart Bookmarks Folder.