Lack of isolation between axes Sometimes I notice that if I manually command a single axis movement (typically Z, when I want better access to the extruder), I observe that several channels move together (and they maybe move slower than I expect). After one 'coupled' movement, subsequent commands have the result I'm expecting.

What happens is as well as the Z-axis moving up, the bed moves forward, and the extruder moves to the right. I have no auto-leveling or anything else non-standard on this printer (dual Z steppers, X, Y, extruder, bed, extruder heat).

It even happens if I simply extrude some of the time (e.g. changing filament after warming up, retract gave me some X movement)

Printer is an ANET-A8, I'm using mainly OctoPrint, but I think I've also observed this with other PC software manual controls.

It doesn't happen often enough for me to have identified any pattern - maybe it only happens if I've not homed first after turning the printer on, but I suspect not.

It's not so much of a problem, as just a question for interest. Also not sure how to tag.
This is easily explained - it's the stepper motors getting powered up. Stepper motors even if not moving are constantly powered up and actively hold the position they are in exactly at the stepping point where they are.

If you power down the machine or if the board disables the stepper drivers to save energy or because the power is offline then the stepper motors can get in between steps. When powering on then the movement is  quite noticeable on some cheaper motors where the inrushing current can kick the motor over multiple steps before it locks down into position.

You can test this, try to move one of the axis manually by hand (not too fast to not damage the board by providing it too much current) if the printer is powered of it does move pretty easily. Then power the printer on, it should still move pretty easily by hand. Now execute one move command on the axis via the printer board. Afterwards you should not be able to move the axis by hand anymore (or at least not without unnecessarily excessive force).