This is the problem if there is no /boot/efi/EFI/ubuntu directory with a grub.cfg with the contents in post #13.

I had the option wrong should have been:
Sorry about that.
grub-install --help will display other options.

If secure boot is disable this grub option allows ubuntu based efi grub not set prefix to the EFI/ubuntu directory.

You never mentioned whether you had any problems (warning/error messages) during the install of Grub nor how exactly you did the install. That could be useful information.

In post 5, your efibootmgr output shows entries for GRUB, arch and pop. If you run the below command, do you see directories for each at that location?

Do you still have Arch installed on another drive? If so, does it boot and if you run grub-mkconfig on it, do you get an entry for Pop OS?

In post 8, you show a grub.cfg file in the /boot/efi/EFI/pop directory with contents pointing to the grub.cfg file on the Pop partitions (hd0,2). What do you see on the actual main grub.cfg file for menuentries on that partition.

I'm not familiar with Pop but wonder how the 'pop' directory appeared on the EFI partition. Was it during the install of Grub from Pop, manually done?

The entry in your initial post which you added to the 40_custom file won't boot from Grub. The path should be to the filesystem partition not to the EFI partition. Also, you indicate in the initial post you ran 'grub-update'. That's a typo correct. Should have been sudo update-grub. Didi you get any output from that? If you edited the 40_custom file and saved the changes and run update-grub, there should have been output.

are you there

pardon me i didnt knew there there was second page, iam working on it now then

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my whole grub was somehow broken after commenting line GRUB_TIMEOUT_STYLE=hidden, selecting a entry from that blueish menu would return "/grub/blablablagrub.cfg couldn't be found, /grub/blablabla.efi couldn't be found" --I definely didn't touched them, seriously they happened on their own maybe purple guy's --no-uefi thing removed them--. and reinstalled everything thanks to archwiki, chroot was a big problem. I again didn't get any error warnings or errors. after adding --no-uefi-secure-boot it worked like a magic, i dont understand anything but it works, thank you for your interest.

https://www.gnu.org/software/grub/manual/grub/grub.html

i will read this now i hope it will help me comprehend this complex bootloader.

That entry does exactly what it says, it does not show any Grub so I don't know what you were seeing on boot.

I do believe that the default grub configuration files are in the /etc/default/grub file however i may be wrong when it comes to PopOS as I haven't used PopOS.