Short answer:
In 22.04:
echo deep | sudo tee -a /sys/power/mem_sleep
If the above doesn't work in 22.04 or if this happens in 22.10, 23.04 or later:
echo s2idle | sudo tee -a /sys/power/mem_sleep
The solution may stop working after kernel updates, and even after reboots, so a script with the needed command can be run at reboot.
The first part is a bit contradictory, because deep should always trigger the long wake-up and s2idle the short one, as said here. Probably something buggy was about in my 22.04 where at least apparently the opposite was sometimes the case.
Long answer:
Very soon after having posted this question I have stumbled upon a solution that seemed to work: on ubuntuforums here, with more advice in reply to that, here.
I don't really understand how this worked, a bug might be involved. That post says that the solution is to switch /sys/power/mem_sleep from s2idle to deep. That was unclear to me because looking up that file it contained this single line:
s2idle [deep]
which means that deep was already selected (!!) — not to mention that, as said above, the opposite behavior was to be expected. —
I have understood what the command does that after asking about it here.
As instructed in the initial ubuntuforums comments , I haven't tried to change that file as such, but I have used the command (based also on the second comment):
echo deep | sudo tee -a /sys/power/mem_sleep
Looking again at that file it seemed unchanged though. Even after restart it was still s2idle [deep], but at that point the wake from suspend was instantaneous! (Which, as far as I know in retrospective was, as said, the opposite of what was expected: deep should mean long wake-up!)
It seems that the file was not changed by that command, but something was changed - related to that file or not.
Changing that to [s2idle] deep with a corresponding command echo s2idle | sudo tee -a /sys/power/mem_sleep (in order to investigate this a bit, as discussed in comments related with the linked question) the 20-second long time waking problem did not re-appear.
Maybe some bug that I cannot track was at play.
After some kernel update the initial problem re-appeared and was fixed in the same way. (Indeed the file /sys/power/mem_sleep was already in the form that the command is supposed to trigger, but the latter is needed nonetheless.)
Update (24 Oct. 2022):
After a new update the above solution didn't work anymore - but the opposite solution did: echo s2idle | sudo tee -a /sys/power/mem_sleep, which amounts to doing the contrary to what my sources prompted me to do.
That seemed bizarre to me at that moment, but now I understand that in fact this was the expected behavior all along: what happened before was odd and buggy, and the new update had fixed that; s2idle is supposed to proved the quick wake up.
After updating to the "normal" 22.10 release, the problem seemed fixed for a while, while the file /sys/power/mem_sleep looked reset to deep. But the 20-sec wake-up delay problem re-appeared, and was fixed as said above under Update 2. Again confirmed after a clean installation of Kubuntu 22.10: after tolerating the problem for a month (just to see if this might be fixed otherwise), the first command didn't help, the second did (February 2023).
Because this problem continues (e.g. in 23.04 - and reappears rather frequently between updates) I have set up a more rapid procedure to run that command from the Application Launcher creating a script file fix_suspend of the form:
#!/bin/sh
echo s2idle | sudo tee -a /sys/power/mem_sleep
and a file ~/.local/share/applications/Fix suspend.desktop containing the line (adapted for Plasma):
Exec=pkexec env DISPLAY=$DISPLAY XAUTHORITY=$XAUTHORITY KDE_SESSION_VERSION=5 KDE_FULL_SESSION=true /path/to/fix_suspend
After a while the solution stopped working after reboot, so I had to make the script run at reboot as indicated in the short answer at the beginning.
