Reduce linkability concerns of the "Search with" contextual search action

We now have a contextual search action "Search with <>", which will be shown if the current page has an associated search engine. E.g. visit de.wikipedia.org and start typing in the urlbar and you will see an action "Search with Wikipedia (de)".

Whilst such an action might be convenient, it currently uses the catch-all circuit to fetch the engine data each time, although the search itself will be performed on the right circuit. See #44179 (closed) and #19741 (closed).

Since this feature is quite prominent and it re-requests the engine data over the catch-all circuit every time it is used, I think we should disable it until we fix the circuit issue.

@donuts, @pierov, @morgan, @ma1 what do you think?

NOTE, the user would still be able to permanently install the search engine using the "This time search with" selector. And it uses the catch-all circuit to install the engine. But I think this case is less prominent and the use of the wrong circuit is limited (I think) and has lower chance for abuse.