@ Susan
I guess I have to questions…
What plugin are you using to enhance the core WordPress search? I ask because WordPress does not use a /search/
endpoint to display results. So this has to be coming from somewhere else.
My guess is whatever is doing this is also possible interfering or incorrectly parsing the Connections shortcode. Really, the except of the search results should do a strip_shortcode() on that excerpt because not doing so can cause all sort of odd thing to happen with shortcodes because the content will be truncated by WordPress when it creates the search excerpt. So, I would consider that a bug with whatever is enhancing the WP search.
The db errors those queries definitely do not make sense. Can you share a screen capture of the Connections : Settings Search tab? I want to duplicate your settings to see if I replicate the errors.