Recently I’ve been logged into a laptop remotely a lot. Logging out from “main” session makes my Gnome on Debian 12 go to suspend after a while. To avoid it you just have to tell:

sudo  dbus-launch gsettings set org.gnome.settings-daemon.plugins.power sleep-inactive-ac-type 'nothing'

Thanks to WinEunuuchs2Unix for the answer I took from Prevent sleep/suspend when not logged in to a specific account; the only change is that GDM on Debian runs as root.

See also https://wiki.debian.org/Suspend#Disable_suspend_and_hibernation:

For systems which should never attempt any type of suspension, these targets can be disabled at the systemd level with the following:

sudo systemctl mask sleep.target suspend.target hibernate.target hybrid-sleep.target

To re-enable hibernate and suspend use the following command:

sudo systemctl unmask sleep.target suspend.target hibernate.target hybrid-sleep.target

A modern alternative approach for disabling suspend and hibernation is to create /etc/systemd/sleep.conf.d/nosuspend.conf as

[Sleep]
AllowSuspend=no
AllowHibernation=no
AllowSuspendThenHibernate=no
AllowHybridSleep=no

The above technique works on Debian 10 Buster and newer. See systemd-sleep.conf(5) for details.

If you just want to prevent suspending when the lid is closed you can set the following options in /etc/systemd/logind.conf:

[Login]
HandleLidSwitch=ignore
HandleLidSwitchDocked=ignore

Then run systemctl restart systemd-logind.service or reboot.