Why the printer is printing while connecting to the system

I had this issue with my M401n and dne before, it's an issue with the network stack WoL (Wake on LAN) not working correctly due to a faulty network stack. The issue is HP never tried to fix it because they were more worried about their HP DS toner DRM for so long that these WoL failing machines went EOL without a fix. The issue is it mostly affects modern devices, especially newer Apple devices that run iOS 16 or newer, given the age of the AirPrint protocol they use.

Unfortunately, there's no way to fix it other than keeping the old settings. I suspect adjusting the sleep times to as late as possible will probably help to a degree, but it's not a permanent fix. It will still occur once the printer sleeps unless you manually wake it up.

Due to this issue, I had to replace mine with an MS621 and other issues like the RAM (processing delays on complex jobs). I did try and avoid it for as long as I could but I had to give up and replace the hardware with a used low PC machine for my sanity. I got it with nearly 14k pages (high 13k range), and it's a far cry better than the M401 ever was. The downside is the PC MATTERS because the fuser is a 200k page service item, so you can't get one with 150k and expect to get off easily. Unless you have a maintenance kit on hand and get the unit at a price that matches the need to service it so soon, don't pick one with a high PC (100k pages or bordering on 100k pages).

I did this on an M426, but this should show you how to change it: