Great! Without too much effort I've got back most of the functionality of the now dead – due to Quantum's limited API – add-on that used to do this. In the end I think this bookmark method is actually easier than having to add to the installed search engines, which is one aspect of Firefox that Mozilla seem to have made unnecessarily complicated in recent years.

The only thing I would suggest is rather than adding a new 'search' item to the context menu, usurp the existing one so there aren't two. Would that be possible?