Really search is something that is designed by each application. While quoted search for an exact term has been taught to us, mostly by Google, it is not the only way to do it. It is however how Thunderbird does it.

However if I type "mitchell baker" into my global search I get advised by Thunderbird in the results pane the results are Results for:mitchell baker if I simply type the two words (which is from the search perspective the same as typing mitchell, baker) thunderbird treats it as Results for:mitchel and baker

This is essentially the same information contained in the relevant support article https://support.mozilla.org/en-US/kb/global-search

My mistake... I did a search and saw a huge list of results for the individual words so I assumed it was not searching for my quoted string when in fact it does both. There is a bit of a UI issue here though. It would be nice if it somehow indicated which results match what I actually was looking for. Or perhaps provide some type of option for exact matches only.