Also with mirrorless cameras, you are viewing the scene as an electronic photo as on a computer screen so if the aperture was always wide open when focusing, the image would many times be too light to be distinguished. With mirrorless one of the differences is that you see the photo as it will be exposed when viewing the scene through the electronic viewfinder. You should have the option to not reflect settings in the viewfinder to partially get away from closed down focusing. I don't have a Canon mirrorless, but feel pretty sure that any brand of mirrorless operates like your Nikon with respect to the aperture size when focusing. Mirrorless= what you see is what you get.
"so if the aperture was always wide open when focusing, the image would many times be too light to be distinguished"
The Live View doesn't work that way in all scenes. Even though the lens set at f/11 is opened to f/5.6, the view is adjusted in brightness amplification to see the effects at f/11 (except for depth of field blurriness).
There's a new setting on the Z6 iii, just added.
a13: Maximum aperture LV= On/Off.
With this a13 off, or with cameras without this setting:
Apertures smaller than f/5.6 will open the lens to f/5.6 for focusing, then close it when the shutter is pressed to take the photo. Apertures wider than f/5.6 will use that aperture for focusing and live view. It's easy to see this looking into the lens when it's set to something like f/11, or to f/2.8.
With a13 =On, the lens is opened to it's max aperture for viewing, no matter what aperture the camera is set to. I know that wedding photographers that work in dim rooms have been waiting for this Z8 feature to be added to other Nikon cameras.
From what I've read, the PDAF autofocus pixels built into the sensor works optimally at f/5.6, using the light rays coming in at opposite angles to the sensor. Do very wide apertures improve the autofocus speed or accuracy, or is it for improved subject detection and an improved scene view, with more light on the sensor?
The downsides to using wide open:
The "i" description in the a13 menu says:
"Maximum aperture is used for live view. Shooting with a smaller aperture may extend release time lag. When "Silent mode" is ON, lag may be further extended".
(In silent mode, the camera turns off sound effects, and minimizes focusing noises coming from the lens, probably by slowing the aperture changing speeds.)