Update: I started a side thread to look into this, and am reporting back here.
Baha noted: "Modern, Monobook, and Vector do track events. Cologne Blue, however, doesn’t and it’s because the search input field doesn’t have the ‘searchInput’ id."
Timo added some extra context: "However our instrumentation isn't applied to searchSuggest in general. It's explicitly applied to the main "search input" field (which is only recognised in Vector and Monobook). So we're not capturing the autocompleted title fields in general (such as on Special:WhatLinksHere). The two (!) search bars in Cologne Blue also fall in this category. They get search suggestions but only because it uses autocompletion in general. If we instrument them all, we'd also get hits form Special:WhatLinksHere and other title input fields.
Monobook, while having a double-button search field, is included in this instrumentation from what I can see. They're not mutually exclusive. You can recognise "primary" search fields (which we instrument) by them having a "Containing [phrase]..." entry at the bottom of the list of options."
I was curious if there would be skew from lack of inclusion of something like Cologne. Looks like based on some queries that Timo ran and the link at
https://meta.wikimedia.org/wiki/Turning_off_outdated_skins/stats Federico pointed out it's probably not too much of a problem. If case people were wondering, the sampling is set at 1:1000 pages for inclusion on the jQuery / ResourceLoader compatible UAs.
Thanks Baha, Federico, and Timo for helping fill in details!
-Adam