Works fine as described. Formerly I used https://addons.mozilla.org/de/firefox/addon/context-search-x/ which is a legacy add-on, but two of its features I wish for "Context Search WebExtension" too:
1. Favicons
2. The uppermost search engine is dedicated as standard. Therefore no need to move the mouse into the pull down menu of various search engines, but click just the main entry "Context Search" (with the magnifier icon) in the context menu and - voilá - the standard search engine is chosen and searching.
3. Of course, grouping would be a nice-to-have feature too for me.

Great job. I was looking for this since no other addon is a webextension. Just one question though, but let's take it to the support page:

https://github.com/NumeriusNegidius/Context-Search/issues/1

combo from 2 legacy add on add to search bar and context search (legacy)

This addon works great. I was hoping that some kind developer would make this extension for WE. A great big thank you for making the transition to WE much easier. I use the ability to search stores and anywhere else I wish several times a day.