Given that this is a chrome.* API, does it still make sense to move it to blink? Or does blink already have support for such cases? (I don't know much about bindings so sorry if this is a naive question)

chrome referes the the UI concept, not to the directory or similar.

there's also eg chromeclient.cpp in blink

Is that actually the case here? chrome.csi looks like a pre Navigation Timing API which doesn't refer to anything in the browser UI.

There is also bug 113048 to remove at least chrome.csi. Given that performance.timing gives much more  detailed results, should we just do that?

if usage is low enough, removing is always an option

Correct, chrome.loadTimes() is a pre-navtiming API. I'd like us to remove both of these. I opened a bug to track removal here: https://bugs.chromium.org/p/chromium/issues/detail?id=621512

Duping this to the bug tracking removing these APIs.