Thanks for this. I've been concerned about QuickSearch disappearing, and this seems to solve it.
I didn't see it in the notes, but if you've already set up QuickSearch, you can simply copy and paste the bookmarks from the Quick Search folder to the Searches folder, and everything seems to work.
With QuickSearch, if you right-clicked with nothing selected, it checked for text in the paste buffer and, if found, offered to search for that text. It's pretty handy, and it would be nice if you could add that.

I like the suggestion by Teko for a "current site search" option for Google, but understand what you say about it deviating from what the add-on does. But what about this approach, which generalises the idea and might fit in a bit more naturally. Currently, the web address has %s replaced by the text selection. What if also %d (say) was replaced by the current domain name. The user could then manually edit the web addresses exactly as they like, for any search engines of their choice. For example, for a Google site search they'd change "%s" to "site:%d %s". This concept could be extended to %u (say) being replaced by the URL. It could then be used to send the whole page to Google Translate, HTML validation services etc. (In this case, the add-on would also need to work with the Context Menu you get when there's no text selection). I realise that it's a bit more work for the user to set up initially, and that there might be technical reasons why it's not suitable - but I thought I'd put the idea forwards.

Good work but how come there are pages e.g. like http://www.thai-language.com/dict/search that is not working?

The setting "When you do a search..." is not saved after you close FF.

Thanks for the hard work, it works very well.
just one suggestion: would you add an option/entry for searching the current site using google (Site Search)?

Have to create a bookmark folder first, and then restart FF, really? Better use the web-extension called "contextual-search".
https://addons.mozilla.org/en-US/firefox/addon/contextual-search/reviews/

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.

I've been using SmartSearch for a long time. Rather than right-clicking a highlighted string and getting only the Google choice afforded by Firefox, I could select which search provider to use. Alas, SmartSearch is a legacy (non-WebExt) add-on so it will die with Firefox 57.

A feature missing in this add-on that SmartSearch has is allowing the user to group their search URLs. That is, under the Search[es] folder, the user could define subfolders. For example, I have all my Google-based searches (general, image, news, maps, etc) grouped under a Searches/Google subfolder. All my Bing search URLs are under a Searches/Bing subfolder. Search providers for which I do not have multiple search types (differentiated by, say, images, news, videos, shopping, etc) have only a single entry so they reside under the Searches folder. This add-on will find all the search URLs under the subfolders (groups) but flattens out its context menu to show all search URLs at the same 1st-level of the context menu. I have 22 search URLs. This makes for a long list. Likely it will get longer. When I intend to search, I already know which one that I want to use so drilling through groups is easier than my eyes rolling up and down scanning a long flat list.

In flattening the list, it is generated in the order the subfolders are alphebetized as subfolders under the Searches folder. So there is still a bit of grouping. However, I would prefer the add-on support subfolders as did the SmartSearch add-on.

Thanks for making a WebExt version of a context search. I would really miss SmartSearch went it gets killed by FF 57.

UPDATE

Woohoo! Subfolders got added in the last release. I was doing some research on an upcoming vacation looking for places to get outdoors (less commercial, cheaper, and more relaxed). I was using Context Search, did some searches, and then realized that I had been selecting my search providers in the subfolders into which I had grouped them. YES! Hurrah to the author, and thanks to Zitronella on mentioning another webext add-on that this author could use as an example of code for context menu subfolders.

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.