Dell laptop Sleep and Hibernation issues

Because you have S0 Modern standby [aka S0 Low power idle], your computer does not sleep. S0 is an idle condition, albeit an aggressive & progressive idle condition.
Your computer is using up power because it is sort-of-on.
There are in effect four Power/Computer states for an S0 Modern standby [aka S0 Low power idle] computer
- Computer on, Monitor on {Work can be done on the computer}
- Computer on, Monitor off {The monitor turning off through Power options settings initiates S0 Modern standby, the progressively severe idle condition that suppresses, amongst other things, Task scheduler tasks}.
- Hibernate
- Off

There is no "Sleep" in the sense that we commonly use the term ["S3 Sleep"].
- This is despite MS leaving the word Sleep dotted around the place such as in the descriptions of the later phases of S0 Modern standby [S0 is progressive. It will increasingly reduce the permitted activities as time passes.].

You could consider disabling S0. Many people have found that disabling S0 automatically enables S3 Sleep despite that "S3 is blocked in the firmware" message [I wasn't one of them. I have disabled S0 and the only sleep state I can now use is hibernation. But that's still better than having S0 rule the roost.].
Disable Modern Standby in Windows 10 and 11 - ElevenForumTutorials
After disabling it, you can run the PowerCfg -a command again to see if S3 has become enabled. If not then you can decide to base your use on just hibernation or revert to using S0 - disabling/enabling S0 only takes a few moments.
- When I disabled S0, I had a WiFi adapter problem which I fixed by reinstalling my WiFi driver from Dell.

I used a sort of halfway house for a while before I finally disabled S0.
- I set my display in Power options to always stay on.
- I set a very dark screensaver to come on after a minute so I wouldn't have the screen staring at me all day if I wasn't actively using the computer.


Best of luck,
Denis

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"so why the hibernation triggers don't work in that mode?"
Sorry, I don't know.
I did not experiment with that aspect of S0.
Your problem indicates that one of the activities that S0 suppresses is reading the low battery threshold levels. That's rather astonishing.

"I could rely solely on the hibernation, but I don't think it's a good idea to hibernate the system every time I close the lid."
It seems a perfectly valid choice to me. What makes you wary of using it?
Whether it's S3 Sleep or hibernation, I restart the computer if I've used either of them half a dozen times during the day.


Have you searched in / asked in the Dell user forums?



Sorry I couldn't help more,
Denis

Papi said:

Each hibernation writes quite large file to the SSD - I'd like to limit that only to the necessary minimum.

Your SSD is probably going to outlive your computer even though you use hibernation.
- All those warnings about minimising SSD use really only applied to early generations of SSD.
- In my current computer, my SSD has been in use for over three years and has only used up 16% of its life. And I have never taken any steps to minimise SSD use.

Denis

Papi said:

it still takes considerably more time to resume from hibernation than idle

Yes.
My main computer, from 2016, takes about 15 seconds to enter hibernation & about 20 seconds to resume from hibernation. [My 2020 desktop computer is much, much quicker.]
I normally go and stick the kettle on when I start using the computers anyway so speed of waking isn't really an issue for me.

Papi said:

Is there any way to control which activities that are supressed in S0 standby?

No.
Well, none that anybody is prepared to tell us mere mortals. The fact that Windows update & the built-in email app run during S0 proves that a method must exist.

Denis

Papi said:

I hoped there are at least some known registers that can change the behaviour.

I take part in every S0-related thread in this forum & ElevenForum. I have never seen any method of altering S0 behaviour other than network connectivity.
You can choose to let your computer stay connected to networks during S0. Turning that off would save you some power.
How to Check if Connected or Disconnected Modern Standby [PowerCfg -a] - TenForumsTutorials
Enable or Disable Network Connectivity in Modern Standby - TenForumsTutorials

Papi said:

It seems I'll have to wait for update that will fix things ...

Intel, MS & hardware makers don't think there is anything in S0 that needs fixing. Which proves that they are all the spawn of Hades.

All the best,
Denis