I didn't know S3 vs S0 but this may be the reason why I never keep my laptop in sleep mode and I prefer to put it in hibernate. What about hibernate? Couldn't it be an alternative to the "legacy sleep"?
Hibernate = S4
https://wiki.archlinux.org/title/Power_management/Suspend_an...
Do you get all your workspace back exactly like it was before, after a shutdown and turn on again ?