Will try to also collect and add profiler data, but while checking it more thoroughly, I have find something.
I use notebook with touchpad and when I use touchpad "click", it of course takes some delay before the whole click action is detected (simple touch can be also start of cursor movement, so it's after losing touch and some debounce delay the click event is produced by the touchpad driver). Don't know how to measure it precisely, but by a feel I would say it takes somewhere between 40-80ms, sometimes slightly over 100ms.
So part of the delay is in the touchpad driver, and it may be in extreme cases the "Ctrl+A" from keyboard comes maybe even milliseconds before the click-event, not sure about that, hopefully you can tell from the profiler data such nuances (whether the action at least came in the correct order).
Still I can recall the firefox is somehow more prone to demonstrate this, like there's sometimes extra 50ms before the bar is active.. or maybe I rarely use this kind of combination of actions in other SW.
address bar vs search bar - hard to tell, it feels like there actually is some difference, like +20-30ms on the search bar, but it's varying a lot (after initial click into both they seem to act quite identically, but the first click after some time of just browsing is sometimes slightly slower).