Do a "cat /sys/kernel/debug/pmc_core/package_cstate_show". You probably have figures for C2 and C3, and C6-C10 states are all zero. C10 is the golden S0ix state that you need for modern sleep.
I have a 13th gen intel Zenbook, and I spent a month fighting the same. My problem was that the bios setting for Intel VMD/Raid cockblocked sleep. If you have any bios options to disable that, or set storage to a more legacy mode, try it.
I'm sure you tried but the definitive option would be a BIOS switch to change it. Sometimes is says S3, sometimes it says Linux sleep (like my personal ThinkPad)
But if you don't have that toggle at all, the firmware probably dumped S3 entirely - especially if it's a relatively new machine and you'll have to lean much more on Hibernate like my new work ThinkPad.
I would investigate whether an older BIOS version still has the S3 toggle since some BIOS updates have removed S3 I believe but a search of forums would probably turn up enough complaints to hit your radar.
Why not just set your laptop to automatically hibernate after it's been in a suspended state for x seconds? That way your system will fully power off after it's been suspended for a while, which would save even more battery compared to S3. With the speed of NVMe drives, resuming from hibernation only takes a couple of seconds on most modern systems.
I remember that on new generations of Intel chips there is no support for S3 at the chipset level, which means that the operating system physically cannot enter the laptop into this mode. On Windows S0ix is better optimized, that's all. Linux has problems with this.
Did you try S3 sleep?
More info here: https://wiki.archlinux.org/title/Power_management/Suspend_and_hibernate#Changing_suspend_method
what does
cat /sys/mem_sleep
give you?
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