I can't get Linux to not drain my laptop battery when the lid is closed. On my M1 Air I can close the lid and come back a week later with maybe a couple percent less battery; on my Framework with PopOS it drains after just a day (default settings).
Same experience here. Also, getting Pop!_OS configured to hibernate looked quite daunting and not worth the effort if you have an existing install.
Probably goes to S2 instead of S3 deep sleep. Had the same issue on microsoft surface (running Linux on it) - i needed to tweak few kernel flags to force it into deep sleep.