There is no "tab to search" feature. The closest thing would be a search keyword (which is a bookmark keyword):

Setup

On the site where you want to send your search:

(A) right-click (one-button: Ctrl+click) the search box (B) click Add Keyword for this Search (C) Edit the name as desired (D) Enter the keyword you want to use for searching, for example, yt for YouTube (example screenshot attached) (E) Click the Save button

Use

In the address bar, type your keyword (e.g., yt) followed by a space followed by your query. Firefox should show the intended search in the address bar drop-down (example screenshot attached).

You also can assign keywords to built-in search engine plugins or others that you add to the one-click icons.

On the Preferences/Options page, click Search in the left column and scroll down to the table of "One-Click Search Engines". In the right column, if you double-click, a text box will appear to type a keyword (press Enter or Return to complete your edit).

Then you can use that keyword to send searches to that site regardless of your default search engine. (Example screenshot attached.)