I'm not a linux expert. And I'm afraid to have problems about Wireless, wired or sound issue because of a system update.
So, I wonder how to stop
AppCenter update notifications?
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The reason AppCenter is auto-starting when you log in is
/etc/xdg/autostart/io.elementary.appcenter-daemon.desktop. I guess you could theoretically remove this (as root), except it'd probably be replaced after an update and you'd be back to where you started.
If you remove AppCenter entirely, which is probably inadvisable, you may want to look into the
unattended-upgrades package as an alternative.
That package adds configuration files to
/etc/apt/apt.conf.d/ which, in principle, apply important security updates automatically and without user intervention… which, in principle, I would prefer to AppCenter incessantly nagging me about them. Most updates are unnecessary if your software is already working the way you like it, but security updates are an exception. My attitude is sure, operating system, do your security stuff without asking me, just don't update any apps that change the whole user interface or whatever.
Lastly, keep in mind that AppCenter's update features are basically a graphical interface on top of
sudo apt update && sudo apt dist-upgrade followed by
flatpak update. Just running those commands in a terminal is sometimes a better experience than waiting for AppCenter to struggle through a bunch of updates, especially if your wifi is spotty.