Provide more server information via Drush

Thanks for the suggestion, that does make sense. I’m happy to review and commit a patch implementing this. (There are unfortunately too many other issues for me to work on this myself.)

In the project I'm working on, a lot of the information actually comes from search_api_solr → - it may be necessary to do something in that module as well as or instead of the main search_api module.

Added some details and verified for DB server.

Thanks, both of you, good start!
However, might it be possible to just re-use BackendInterface::viewSettings() to get backend-specific additional columns? Just magically transforming the settings key into a label might work well in most cases, and in English, but is not translatable and also not very flexible. Better to use something that was meant to be user-facing.