autofocus – Which actions in the camera menu/settings change the focus and which do not?

None of the settings you mention will change the lens focussing – but changing the focal length on a zoom lens definitely will.

Previous answer, obviated by comments & question edit
This is almost moot unless you switch off the AF mechanism in the half-press by one of the following methods.

With standard settings, every time you half-press it will refocus, so anything else you do in between will require another half-press, focus, shot.
You cannot avoid the half-press no matter how fast you do it, it will check or refocus every time you press it, unless you switch it off.

The way to avoid this is by using back button focus instead, so only pressing the back button will focus, pressing the shutter will simply take the photo.

You can set this up in settings – I also moved mine to the Quick menu to save having to dig for it every time. You can lock focus &/or exposure, jointly or separately.
This is from the D5500 manual. I doubt the D5600 is much different…

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Alternatively, if your lens supports it, you could just flip the physical switch on the side from M/A to M.
If not, you can disable it in the main shoot menu on the rear of the camera.