Sleep mode consumes as much as battery as when laptop is in use

I could solve the issue. I will answer my own question hoping it helps anyone else facing the same problem.

The Lenovo X1 Carbon 6th gen uses a new sleeping state (Si03, Windows Modern Standby) instead of the traditional S3 sleep state. Linux does not support that new state.

The workaround presented here worked well: https://delta-xi.net/#056