Hey, thanks a lot for the answer 
What is the output of your cat /sys/power/mem_sleep
?
Right now it says:
> cat /sys/power/mem_sleep
[s2idle] deep
After the fresh install I followed the the guide on the framework page
With the recommended power settings
sudo kernelstub -a nvme.noacpi=1
sudo kernelstub -a mem_sleep_default=deep
However it took very long to wake up from sleep (about 25 seconds), this is when I wrote the issue here.
One thing I tried yesterday was to use
94 sudo kernelstub -a mem_sleep_default=shallow
95 sudo kernelstub -d mem_sleep_default=deep
the laptop had 75% battery when going to sleep and 49% when I woke up the next morning. However it improved the wake up time. I will edit this post with the data from this night.
Appendix
After the finishing the setup on the install page the output looked like this:
caspar@pop-os:~$ sudo kernelstub -p
kernelstub.Config : INFO Looking for configuration...
kernelstub : INFO System information:
OS:..................Pop!_OS 22.04
Root partition:....../dev/dm-1
Root FS UUID:........f553b310-f877-4a84-83a6-2fce6a439b6d
ESP Path:............/boot/efi
ESP Partition:......./dev/nvme0n1p1
ESP Partition #:.....1
NVRAM entry #:.......-1
Boot Variable #:.....0000
Kernel Boot Options:.systemd.show_status=false nvme.noacpi=1 mem_sleep_default=deep loglevel=0 quiet splash
Kernel Image Path:.../boot/vmlinuz-6.0.12-76060006-generic
Initrd Image Path:.../boot/initrd.img-6.0.12-76060006-generic
Force-overwrite:.....False
kernelstub : INFO Configuration details:
ESP Location:................../boot/efi
Management Mode:...............True
Install Loader configuration:..True
Configuration version:.........3
Now it looks like this:
Place your right index finger on the fingerprint reader
kernelstub.Config : INFO Looking for configuration...
kernelstub : INFO System information:
OS:..................Pop!_OS 22.04
Root partition:....../dev/dm-1
Root FS UUID:........f553b310-f877-4a84-83a6-2fce6a439b6d
ESP Path:............/boot/efi
ESP Partition:......./dev/nvme0n1p1
ESP Partition #:.....1
NVRAM entry #:.......-1
Boot Variable #:.....0000
Kernel Boot Options:.systemd.show_status=false mem_sleep_default=shallow quiet nvme.noacpi=1 loglevel=0 splash
Kernel Image Path:.../boot/vmlinuz-6.0.12-76060006-generic
Initrd Image Path:.../boot/initrd.img-6.0.12-76060006-generic
Force-overwrite:.....False
kernelstub : INFO Configuration details:
ESP Location:................../boot/efi
Management Mode:...............True
Install Loader configuration:..True
Configuration version:.........3