dkms status seems to confirm exactly what you are saying.
$ dkms status
nvidia, 390.141, 5.8.0-40-generic, x86_64: installed (WARNING! Diff between built and installed module!) (WARNING! Diff between built and installed module!) (WARNING! Diff between built and installed module!)
update-initramfs -u did not issue an error, but after a reboot nothing has changed. dkms status seems to give the same response as before.
$ sudo update-initramfs -u
update-initramfs: Generating /boot/initrd.img-5.8.0-40-generic