Thank you. However, your use of ‘a’ and ‘b’, and your omission of code formatting, makes your post a little hard to read. So, to aid clarity, let me list (/reformulate) the code and settings at issue - thusly.
The string to be added to one’s boot string is mem_sleep_default=deep.
The command to update-grub is: sudo update-grub.
(Incidentally, one can use the program grub-customizer for this stuff. One will need to find a way to install that program. On Ubuntu 24, and distros based on Ubuntu 24, there is a PPA advertised on the 'net.)
The verification command is cat /sys/power/mem_sleep.
Also/but: on my AMD Framework-13, the verification fails, i.e., deep sleep appears to be unavailable (even after telling the ‘tlp’ program to use deep sleep). EDIT: ah, this thread says deep sleep is not supported on Framework’s AMD laptops.