The only way I know to search for folders only is via the left pane in the Library.
If you type the first letter(s) quickly enough then you go through each result and if you type the letters another time to the next result.
This also works in the Bookmarks sidebar, but that also finds bookmarks.
It is not really convenient, but at least it works.

@cor-el, Thanks for your reply -- I am hoping there could be an actual folder search. Surely I'm not the first person to need this.

I see this new extension ("Awesome Search Extension") without many users yet - it's unclear to me if this has the feature I need, but maybe it's worth a try?

https://addons.mozilla.org/en-US/firefox/addon/awesome-search-extension/

The aforementioned addon *does* let you search for and find bookmark folders, albeit by typing the search text into the browser address bar. Not the best implementation for this particular need, so still looking for a better answer, but that addon is indeed one way to do it.

Edit: I read this question wrong. Never mind

Yes. "Show Parent Folder": https://addons.mozilla.org/firefox/ad.../show-parent-folder/. There is a setting in the extension's Options dialog to show the full hierarchy if your bookmarks are deeply nested.

Similar old thread: after i search for an item in my bookmarks, how do I get Firefox to show me where in my bookmarks the item is located?

@jscher2000 thanks anyway!

No addons, sorry.

An expedient could be to export bookmarks in html file, open the file with firefox and search in the page.